Deck 9: Differential Equations

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سؤال
Solve the initial-value problem. <strong>Solve the initial-value problem.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>

A) <strong>Solve the initial-value problem.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Solve the initial-value problem.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Solve the initial-value problem.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Solve the initial-value problem.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Solve the initial-value problem.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
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سؤال
Solve the differential equation. <strong>Solve the differential equation.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>

A) <strong>Solve the differential equation.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Solve the differential equation.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Solve the differential equation.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Solve the differential equation.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Solve the differential equation.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
Solve the initial-value problem. <strong>Solve the initial-value problem.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>

A) <strong>Solve the initial-value problem.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Solve the initial-value problem.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Solve the initial-value problem.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Solve the initial-value problem.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Solve the initial-value problem.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
Determine whether the differential equation is linear. <strong>Determine whether the differential equation is linear.  </strong> A)the equation is not linear B)the equation is linear <div style=padding-top: 35px>

A)the equation is not linear
B)the equation is linear
سؤال
Solve the differential equation. <strong>Solve the differential equation.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>

A) <strong>Solve the differential equation.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Solve the differential equation.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Solve the differential equation.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Solve the differential equation.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Solve the differential equation.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
In the circuit shown in Figure, a generator supplies a voltage of <strong>In the circuit shown in Figure, a generator supplies a voltage of   volts, the inductance is 2 H, the resistance is 40   , and   . Find the current 0.2 s after the switch is closed. Round your answer to two decimal places.  </strong> A) 0.75 A B)   C)   D)   E)   <div style=padding-top: 35px> volts, the inductance is 2 H, the resistance is 40 <strong>In the circuit shown in Figure, a generator supplies a voltage of   volts, the inductance is 2 H, the resistance is 40   , and   . Find the current 0.2 s after the switch is closed. Round your answer to two decimal places.  </strong> A) 0.75 A B)   C)   D)   E)   <div style=padding-top: 35px> , and <strong>In the circuit shown in Figure, a generator supplies a voltage of   volts, the inductance is 2 H, the resistance is 40   , and   . Find the current 0.2 s after the switch is closed. Round your answer to two decimal places.  </strong> A) 0.75 A B)   C)   D)   E)   <div style=padding-top: 35px> . Find the current 0.2 s after the switch is closed. Round your answer to two decimal places. <strong>In the circuit shown in Figure, a generator supplies a voltage of   volts, the inductance is 2 H, the resistance is 40   , and   . Find the current 0.2 s after the switch is closed. Round your answer to two decimal places.  </strong> A) 0.75 A B)   C)   D)   E)   <div style=padding-top: 35px>

A) 0.75 A
B) <strong>In the circuit shown in Figure, a generator supplies a voltage of   volts, the inductance is 2 H, the resistance is 40   , and   . Find the current 0.2 s after the switch is closed. Round your answer to two decimal places.  </strong> A) 0.75 A B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>In the circuit shown in Figure, a generator supplies a voltage of   volts, the inductance is 2 H, the resistance is 40   , and   . Find the current 0.2 s after the switch is closed. Round your answer to two decimal places.  </strong> A) 0.75 A B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>In the circuit shown in Figure, a generator supplies a voltage of   volts, the inductance is 2 H, the resistance is 40   , and   . Find the current 0.2 s after the switch is closed. Round your answer to two decimal places.  </strong> A) 0.75 A B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>In the circuit shown in Figure, a generator supplies a voltage of   volts, the inductance is 2 H, the resistance is 40   , and   . Find the current 0.2 s after the switch is closed. Round your answer to two decimal places.  </strong> A) 0.75 A B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
An object with mass m is dropped from rest and we assume that the air resistance is proportional to the speed of the object. If An object with mass m is dropped from rest and we assume that the air resistance is proportional to the speed of the object. If   is the distance dropped after t seconds, then the speed is   and the acceleration is   . If g is the acceleration due to gravity, then the downward force on the object is   , where c is a positive constant, and Newton's Second Law gives   . Find the limiting velocity.<div style=padding-top: 35px> is the distance dropped after t seconds, then the speed is An object with mass m is dropped from rest and we assume that the air resistance is proportional to the speed of the object. If   is the distance dropped after t seconds, then the speed is   and the acceleration is   . If g is the acceleration due to gravity, then the downward force on the object is   , where c is a positive constant, and Newton's Second Law gives   . Find the limiting velocity.<div style=padding-top: 35px> and the acceleration is An object with mass m is dropped from rest and we assume that the air resistance is proportional to the speed of the object. If   is the distance dropped after t seconds, then the speed is   and the acceleration is   . If g is the acceleration due to gravity, then the downward force on the object is   , where c is a positive constant, and Newton's Second Law gives   . Find the limiting velocity.<div style=padding-top: 35px> . If g is the acceleration due to gravity, then the downward force on the object is An object with mass m is dropped from rest and we assume that the air resistance is proportional to the speed of the object. If   is the distance dropped after t seconds, then the speed is   and the acceleration is   . If g is the acceleration due to gravity, then the downward force on the object is   , where c is a positive constant, and Newton's Second Law gives   . Find the limiting velocity.<div style=padding-top: 35px> , where c is a positive constant, and Newton's Second Law gives An object with mass m is dropped from rest and we assume that the air resistance is proportional to the speed of the object. If   is the distance dropped after t seconds, then the speed is   and the acceleration is   . If g is the acceleration due to gravity, then the downward force on the object is   , where c is a positive constant, and Newton's Second Law gives   . Find the limiting velocity.<div style=padding-top: 35px> .
Find the limiting velocity.
سؤال
Solve the initial-value problem. <strong>Solve the initial-value problem.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>

A) <strong>Solve the initial-value problem.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Solve the initial-value problem.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Solve the initial-value problem.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Solve the initial-value problem.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Solve the initial-value problem.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
We modeled populations of aphids and ladybugs with a Lotka-Volterra system. Suppose we modify those equations as follows: <strong>We modeled populations of aphids and ladybugs with a Lotka-Volterra system. Suppose we modify those equations as follows:   ,  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> , <strong>We modeled populations of aphids and ladybugs with a Lotka-Volterra system. Suppose we modify those equations as follows:   ,  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>

A) <strong>We modeled populations of aphids and ladybugs with a Lotka-Volterra system. Suppose we modify those equations as follows:   ,  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>We modeled populations of aphids and ladybugs with a Lotka-Volterra system. Suppose we modify those equations as follows:   ,  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>We modeled populations of aphids and ladybugs with a Lotka-Volterra system. Suppose we modify those equations as follows:   ,  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>We modeled populations of aphids and ladybugs with a Lotka-Volterra system. Suppose we modify those equations as follows:   ,  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>We modeled populations of aphids and ladybugs with a Lotka-Volterra system. Suppose we modify those equations as follows:   ,  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
A phase trajectory is shown for populations of rabbits <strong>A phase trajectory is shown for populations of rabbits   and foxes   . Describe how each population changes as time goes by.   Select the correct statement.</strong> A)At   the population of foxes reaches a minimum of about 30. B)At   the number of rabbits rebounds to 500. C)At   the number of foxes reaches a maximum of about 2400. <div style=padding-top: 35px> and foxes <strong>A phase trajectory is shown for populations of rabbits   and foxes   . Describe how each population changes as time goes by.   Select the correct statement.</strong> A)At   the population of foxes reaches a minimum of about 30. B)At   the number of rabbits rebounds to 500. C)At   the number of foxes reaches a maximum of about 2400. <div style=padding-top: 35px> . Describe how each population changes as time goes by. <strong>A phase trajectory is shown for populations of rabbits   and foxes   . Describe how each population changes as time goes by.   Select the correct statement.</strong> A)At   the population of foxes reaches a minimum of about 30. B)At   the number of rabbits rebounds to 500. C)At   the number of foxes reaches a maximum of about 2400. <div style=padding-top: 35px> Select the correct statement.

A)At <strong>A phase trajectory is shown for populations of rabbits   and foxes   . Describe how each population changes as time goes by.   Select the correct statement.</strong> A)At   the population of foxes reaches a minimum of about 30. B)At   the number of rabbits rebounds to 500. C)At   the number of foxes reaches a maximum of about 2400. <div style=padding-top: 35px> the population of foxes reaches a minimum of about 30.
B)At <strong>A phase trajectory is shown for populations of rabbits   and foxes   . Describe how each population changes as time goes by.   Select the correct statement.</strong> A)At   the population of foxes reaches a minimum of about 30. B)At   the number of rabbits rebounds to 500. C)At   the number of foxes reaches a maximum of about 2400. <div style=padding-top: 35px> the number of rabbits rebounds to 500.
C)At <strong>A phase trajectory is shown for populations of rabbits   and foxes   . Describe how each population changes as time goes by.   Select the correct statement.</strong> A)At   the population of foxes reaches a minimum of about 30. B)At   the number of rabbits rebounds to 500. C)At   the number of foxes reaches a maximum of about 2400. <div style=padding-top: 35px> the number of foxes reaches a maximum of about 2400.
سؤال
Which of the following functions is a solution of the differential equation? <strong>Which of the following functions is a solution of the differential equation?   </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>

A) <strong>Which of the following functions is a solution of the differential equation?   </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Which of the following functions is a solution of the differential equation?   </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Which of the following functions is a solution of the differential equation?   </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Which of the following functions is a solution of the differential equation?   </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Which of the following functions is a solution of the differential equation?   </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
Solve the differential equation. <strong>Solve the differential equation.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>

A) <strong>Solve the differential equation.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Solve the differential equation.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Solve the differential equation.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Solve the differential equation.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Solve the differential equation.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
Solve the differential equation. Solve the differential equation.  <div style=padding-top: 35px>
سؤال
Determine whether the differential equation is linear. Determine whether the differential equation is linear.  <div style=padding-top: 35px>
سؤال
Solve the initial-value problem. <strong>Solve the initial-value problem.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>

A) <strong>Solve the initial-value problem.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Solve the initial-value problem.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Solve the initial-value problem.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Solve the initial-value problem.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Solve the initial-value problem.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
Solve the initial-value problem. Solve the initial-value problem.  <div style=padding-top: 35px>
سؤال
Solve the initial-value problem. Solve the initial-value problem.  <div style=padding-top: 35px>
سؤال
Find the solution of the initial-value problem and use it to find the population when Find the solution of the initial-value problem and use it to find the population when   .  <div style=padding-top: 35px> . Find the solution of the initial-value problem and use it to find the population when   .  <div style=padding-top: 35px>
سؤال
Let <strong>Let   be the performance level of someone learning a skill as a function of the training time t. The graph of P is called a learning curve. We propose the differential equation   as a reasonable model for learning, where r is a positive constant. Solve it as a linear differential equation.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> be the performance level of someone learning a skill as a function of the training time t. The graph of P is called a learning curve. We propose the differential equation <strong>Let   be the performance level of someone learning a skill as a function of the training time t. The graph of P is called a learning curve. We propose the differential equation   as a reasonable model for learning, where r is a positive constant. Solve it as a linear differential equation.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> as a reasonable model for learning, where r is a positive constant. Solve it as a linear differential equation.

A) <strong>Let   be the performance level of someone learning a skill as a function of the training time t. The graph of P is called a learning curve. We propose the differential equation   as a reasonable model for learning, where r is a positive constant. Solve it as a linear differential equation.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Let   be the performance level of someone learning a skill as a function of the training time t. The graph of P is called a learning curve. We propose the differential equation   as a reasonable model for learning, where r is a positive constant. Solve it as a linear differential equation.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Let   be the performance level of someone learning a skill as a function of the training time t. The graph of P is called a learning curve. We propose the differential equation   as a reasonable model for learning, where r is a positive constant. Solve it as a linear differential equation.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Let   be the performance level of someone learning a skill as a function of the training time t. The graph of P is called a learning curve. We propose the differential equation   as a reasonable model for learning, where r is a positive constant. Solve it as a linear differential equation.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Let   be the performance level of someone learning a skill as a function of the training time t. The graph of P is called a learning curve. We propose the differential equation   as a reasonable model for learning, where r is a positive constant. Solve it as a linear differential equation.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
Solve the initial-value problem. Solve the initial-value problem.  <div style=padding-top: 35px>
سؤال
Suppose that a population grows according to a logistic model with carrying capacity <strong>Suppose that a population grows according to a logistic model with carrying capacity   and   per year. Choose the logistic differential equation for these data.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> and <strong>Suppose that a population grows according to a logistic model with carrying capacity   and   per year. Choose the logistic differential equation for these data.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> per year. Choose the logistic differential equation for these data.

A) <strong>Suppose that a population grows according to a logistic model with carrying capacity   and   per year. Choose the logistic differential equation for these data.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Suppose that a population grows according to a logistic model with carrying capacity   and   per year. Choose the logistic differential equation for these data.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Suppose that a population grows according to a logistic model with carrying capacity   and   per year. Choose the logistic differential equation for these data.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Suppose that a population grows according to a logistic model with carrying capacity   and   per year. Choose the logistic differential equation for these data.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Suppose that a population grows according to a logistic model with carrying capacity   and   per year. Choose the logistic differential equation for these data.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
Let Let   . What are the equilibrium solutions?<div style=padding-top: 35px> .
What are the equilibrium solutions?
سؤال
The population of the world was about 5.3 billion in 1990. Birth rates in the 1990s range from 35 to 40 million per year and death rates range from 15 to 20 million per year. Let's assume that the carrying capacity for world population is 100 billion. Use the logistic model to predict the world population in the 2,450 year. Calculate your answer in billions to one decimal place. (Because the initial population is small compared to the carrying capacity, you can take k to be an estimate of the initial relative growth rate.)

A)59.2 billion
B)32.9 billion
C)78.3 billion
D)17.1 billion
E)24.1 billion
سؤال
The rate of change of atmospheric pressure P with respect to altitude h is proportional to P provided that the temperature is constant. At The rate of change of atmospheric pressure P with respect to altitude h is proportional to P provided that the temperature is constant. At   the pressure is   at sea level and   at   . What is the pressure at an altitude of   ?<div style=padding-top: 35px> the pressure is The rate of change of atmospheric pressure P with respect to altitude h is proportional to P provided that the temperature is constant. At   the pressure is   at sea level and   at   . What is the pressure at an altitude of   ?<div style=padding-top: 35px> at sea level and The rate of change of atmospheric pressure P with respect to altitude h is proportional to P provided that the temperature is constant. At   the pressure is   at sea level and   at   . What is the pressure at an altitude of   ?<div style=padding-top: 35px> at The rate of change of atmospheric pressure P with respect to altitude h is proportional to P provided that the temperature is constant. At   the pressure is   at sea level and   at   . What is the pressure at an altitude of   ?<div style=padding-top: 35px> . What is the pressure at an altitude of The rate of change of atmospheric pressure P with respect to altitude h is proportional to P provided that the temperature is constant. At   the pressure is   at sea level and   at   . What is the pressure at an altitude of   ?<div style=padding-top: 35px> ?
سؤال
Let c be a positive number. A differential equation of the form Let c be a positive number. A differential equation of the form   where k is a positive constant, is called a doomsday equation because the exponent in the expression   is larger than the exponent 1for natural growth. An especially prolific breed of rabbits has the growth term   . If   such rabbits breed initially and the warren has   rabbits after   months, then when is doomsday?<div style=padding-top: 35px> where k is a positive constant, is called a doomsday equation because the exponent in the expression Let c be a positive number. A differential equation of the form   where k is a positive constant, is called a doomsday equation because the exponent in the expression   is larger than the exponent 1for natural growth. An especially prolific breed of rabbits has the growth term   . If   such rabbits breed initially and the warren has   rabbits after   months, then when is doomsday?<div style=padding-top: 35px> is larger than the exponent 1for natural growth. An especially prolific breed of rabbits has the growth term Let c be a positive number. A differential equation of the form   where k is a positive constant, is called a doomsday equation because the exponent in the expression   is larger than the exponent 1for natural growth. An especially prolific breed of rabbits has the growth term   . If   such rabbits breed initially and the warren has   rabbits after   months, then when is doomsday?<div style=padding-top: 35px> . If Let c be a positive number. A differential equation of the form   where k is a positive constant, is called a doomsday equation because the exponent in the expression   is larger than the exponent 1for natural growth. An especially prolific breed of rabbits has the growth term   . If   such rabbits breed initially and the warren has   rabbits after   months, then when is doomsday?<div style=padding-top: 35px> such rabbits breed initially and the warren has Let c be a positive number. A differential equation of the form   where k is a positive constant, is called a doomsday equation because the exponent in the expression   is larger than the exponent 1for natural growth. An especially prolific breed of rabbits has the growth term   . If   such rabbits breed initially and the warren has   rabbits after   months, then when is doomsday?<div style=padding-top: 35px> rabbits after Let c be a positive number. A differential equation of the form   where k is a positive constant, is called a doomsday equation because the exponent in the expression   is larger than the exponent 1for natural growth. An especially prolific breed of rabbits has the growth term   . If   such rabbits breed initially and the warren has   rabbits after   months, then when is doomsday?<div style=padding-top: 35px> months, then when is doomsday?
سؤال
Consider the differential equation Consider the differential equation   as a model for a fish population, where t is measured in weeks and c is a constant. For what values of c does the fish population always die out?<div style=padding-top: 35px> as a model for a fish population, where t is measured in weeks and c is a constant. For what values of c does the fish population always die out?
سؤال
One model for the spread of a rumor is that the rate of spread is proportional to the product of the fraction of the population who have heard the rumor and the fraction who have not heard the rumor. Let's assume that the constant of proportionality is One model for the spread of a rumor is that the rate of spread is proportional to the product of the fraction of the population who have heard the rumor and the fraction who have not heard the rumor. Let's assume that the constant of proportionality is   . Write a differential equation that is satisfied by y.<div style=padding-top: 35px> . Write a differential equation that is satisfied by y.
سؤال
The Pacific halibut fishery has been modeled by the differential equation The Pacific halibut fishery has been modeled by the differential equation   where   is the biomass (the total mass of the members of the population) in kilograms at time t (measured in years), the carrying capacity is estimated to be   and   per year. If   , find the biomass a year later.<div style=padding-top: 35px> where The Pacific halibut fishery has been modeled by the differential equation   where   is the biomass (the total mass of the members of the population) in kilograms at time t (measured in years), the carrying capacity is estimated to be   and   per year. If   , find the biomass a year later.<div style=padding-top: 35px> is the biomass (the total mass of the members of the population) in kilograms at time t (measured in years), the carrying capacity is estimated to be The Pacific halibut fishery has been modeled by the differential equation   where   is the biomass (the total mass of the members of the population) in kilograms at time t (measured in years), the carrying capacity is estimated to be   and   per year. If   , find the biomass a year later.<div style=padding-top: 35px> and The Pacific halibut fishery has been modeled by the differential equation   where   is the biomass (the total mass of the members of the population) in kilograms at time t (measured in years), the carrying capacity is estimated to be   and   per year. If   , find the biomass a year later.<div style=padding-top: 35px> per year. If The Pacific halibut fishery has been modeled by the differential equation   where   is the biomass (the total mass of the members of the population) in kilograms at time t (measured in years), the carrying capacity is estimated to be   and   per year. If   , find the biomass a year later.<div style=padding-top: 35px> , find the biomass a year later.
سؤال
Suppose that a population grows according to a logistic model with carrying capacity Suppose that a population grows according to a logistic model with carrying capacity   and   per year. Write the logistic differential equation for these data.<div style=padding-top: 35px> and Suppose that a population grows according to a logistic model with carrying capacity   and   per year. Write the logistic differential equation for these data.<div style=padding-top: 35px> per year. Write the logistic differential equation for these data.
سؤال
Let c be a positive number. A differential equation of the form <strong>Let c be a positive number. A differential equation of the form   where k is a positive constant is called a doomsday equation because the exponent in the expression   is larger than the exponent 1 for natural growth. An especially prolific breed of rabbits has the growth term   . If   such rabbits breed initially and the warren has   rabbits after   months, then when is doomsday?</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> where k is a positive constant is called a doomsday equation because the exponent in the expression <strong>Let c be a positive number. A differential equation of the form   where k is a positive constant is called a doomsday equation because the exponent in the expression   is larger than the exponent 1 for natural growth. An especially prolific breed of rabbits has the growth term   . If   such rabbits breed initially and the warren has   rabbits after   months, then when is doomsday?</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> is larger than the exponent 1 for natural growth. An especially prolific breed of rabbits has the growth term <strong>Let c be a positive number. A differential equation of the form   where k is a positive constant is called a doomsday equation because the exponent in the expression   is larger than the exponent 1 for natural growth. An especially prolific breed of rabbits has the growth term   . If   such rabbits breed initially and the warren has   rabbits after   months, then when is doomsday?</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> . If <strong>Let c be a positive number. A differential equation of the form   where k is a positive constant is called a doomsday equation because the exponent in the expression   is larger than the exponent 1 for natural growth. An especially prolific breed of rabbits has the growth term   . If   such rabbits breed initially and the warren has   rabbits after   months, then when is doomsday?</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> such rabbits breed initially and the warren has <strong>Let c be a positive number. A differential equation of the form   where k is a positive constant is called a doomsday equation because the exponent in the expression   is larger than the exponent 1 for natural growth. An especially prolific breed of rabbits has the growth term   . If   such rabbits breed initially and the warren has   rabbits after   months, then when is doomsday?</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> rabbits after <strong>Let c be a positive number. A differential equation of the form   where k is a positive constant is called a doomsday equation because the exponent in the expression   is larger than the exponent 1 for natural growth. An especially prolific breed of rabbits has the growth term   . If   such rabbits breed initially and the warren has   rabbits after   months, then when is doomsday?</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> months, then when is doomsday?

A) <strong>Let c be a positive number. A differential equation of the form   where k is a positive constant is called a doomsday equation because the exponent in the expression   is larger than the exponent 1 for natural growth. An especially prolific breed of rabbits has the growth term   . If   such rabbits breed initially and the warren has   rabbits after   months, then when is doomsday?</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Let c be a positive number. A differential equation of the form   where k is a positive constant is called a doomsday equation because the exponent in the expression   is larger than the exponent 1 for natural growth. An especially prolific breed of rabbits has the growth term   . If   such rabbits breed initially and the warren has   rabbits after   months, then when is doomsday?</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Let c be a positive number. A differential equation of the form   where k is a positive constant is called a doomsday equation because the exponent in the expression   is larger than the exponent 1 for natural growth. An especially prolific breed of rabbits has the growth term   . If   such rabbits breed initially and the warren has   rabbits after   months, then when is doomsday?</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Let c be a positive number. A differential equation of the form   where k is a positive constant is called a doomsday equation because the exponent in the expression   is larger than the exponent 1 for natural growth. An especially prolific breed of rabbits has the growth term   . If   such rabbits breed initially and the warren has   rabbits after   months, then when is doomsday?</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Let c be a positive number. A differential equation of the form   where k is a positive constant is called a doomsday equation because the exponent in the expression   is larger than the exponent 1 for natural growth. An especially prolific breed of rabbits has the growth term   . If   such rabbits breed initially and the warren has   rabbits after   months, then when is doomsday?</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
A curve passes through the point <strong>A curve passes through the point   and has the property that the slope of the curve at every point P is   times the y-coordinate P. What is the equation of the curve?</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> and has the property that the slope of the curve at every point P is <strong>A curve passes through the point   and has the property that the slope of the curve at every point P is   times the y-coordinate P. What is the equation of the curve?</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> times the y-coordinate P. What is the equation of the curve?

A) <strong>A curve passes through the point   and has the property that the slope of the curve at every point P is   times the y-coordinate P. What is the equation of the curve?</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>A curve passes through the point   and has the property that the slope of the curve at every point P is   times the y-coordinate P. What is the equation of the curve?</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>A curve passes through the point   and has the property that the slope of the curve at every point P is   times the y-coordinate P. What is the equation of the curve?</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>A curve passes through the point   and has the property that the slope of the curve at every point P is   times the y-coordinate P. What is the equation of the curve?</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>A curve passes through the point   and has the property that the slope of the curve at every point P is   times the y-coordinate P. What is the equation of the curve?</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
Biologists stocked a lake with Biologists stocked a lake with   fish and estimated the carrying capacity (the maximal population for the fish of that species in that lake) to be   . The number of fish tripled in the first year. Assuming that the size of the fish population satisfies the logistic equation, find an expression for the size of the population after t years.<div style=padding-top: 35px> fish and estimated the carrying capacity (the maximal population for the fish of that species in that lake) to be Biologists stocked a lake with   fish and estimated the carrying capacity (the maximal population for the fish of that species in that lake) to be   . The number of fish tripled in the first year. Assuming that the size of the fish population satisfies the logistic equation, find an expression for the size of the population after t years.<div style=padding-top: 35px> . The number of fish tripled in the first year. Assuming that the size of the fish population satisfies the logistic equation, find an expression for the size of the population after t years.
سؤال
Solve the differential equation. <strong>Solve the differential equation.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>

A) <strong>Solve the differential equation.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Solve the differential equation.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Solve the differential equation.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Solve the differential equation.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Solve the differential equation.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
The population of the world was about 5.3 billion in 1990. Birth rates in the 1990s range from 35 to 40 million per year and death rates range from 15 to 20 million per year. Let's assume that the carrying capacity for world population is 100 billion. Use the logistic model to predict the world population in the 2,450 year. Calculate your answer in billions to one decimal place. (Because the initial population is small compared to the carrying capacity, you can take k to be an estimate of the initial relative growth rate.)

A)24.1 billion
B)32.9 billion
C)59.2 billion
D)78.3 billion
E)17.1 billion
سؤال
One model for the spread of an epidemic is that the rate of spread is jointly proportional to the number of infected people and the number of uninfected people. In an isolated town of <strong>One model for the spread of an epidemic is that the rate of spread is jointly proportional to the number of infected people and the number of uninfected people. In an isolated town of   inhabitants,   people have a disease at the beginning of the week and   have it at the end of the week. How long does it take for   of the population to be infected?</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> inhabitants, <strong>One model for the spread of an epidemic is that the rate of spread is jointly proportional to the number of infected people and the number of uninfected people. In an isolated town of   inhabitants,   people have a disease at the beginning of the week and   have it at the end of the week. How long does it take for   of the population to be infected?</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> people have a disease at the beginning of the week and <strong>One model for the spread of an epidemic is that the rate of spread is jointly proportional to the number of infected people and the number of uninfected people. In an isolated town of   inhabitants,   people have a disease at the beginning of the week and   have it at the end of the week. How long does it take for   of the population to be infected?</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> have it at the end of the week. How long does it take for <strong>One model for the spread of an epidemic is that the rate of spread is jointly proportional to the number of infected people and the number of uninfected people. In an isolated town of   inhabitants,   people have a disease at the beginning of the week and   have it at the end of the week. How long does it take for   of the population to be infected?</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> of the population to be infected?

A) <strong>One model for the spread of an epidemic is that the rate of spread is jointly proportional to the number of infected people and the number of uninfected people. In an isolated town of   inhabitants,   people have a disease at the beginning of the week and   have it at the end of the week. How long does it take for   of the population to be infected?</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>One model for the spread of an epidemic is that the rate of spread is jointly proportional to the number of infected people and the number of uninfected people. In an isolated town of   inhabitants,   people have a disease at the beginning of the week and   have it at the end of the week. How long does it take for   of the population to be infected?</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>One model for the spread of an epidemic is that the rate of spread is jointly proportional to the number of infected people and the number of uninfected people. In an isolated town of   inhabitants,   people have a disease at the beginning of the week and   have it at the end of the week. How long does it take for   of the population to be infected?</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>One model for the spread of an epidemic is that the rate of spread is jointly proportional to the number of infected people and the number of uninfected people. In an isolated town of   inhabitants,   people have a disease at the beginning of the week and   have it at the end of the week. How long does it take for   of the population to be infected?</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>One model for the spread of an epidemic is that the rate of spread is jointly proportional to the number of infected people and the number of uninfected people. In an isolated town of   inhabitants,   people have a disease at the beginning of the week and   have it at the end of the week. How long does it take for   of the population to be infected?</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
A sum of <strong>A sum of   is invested at   interest. If   is the amount of the investment at time t for the case of continuous compounding, write a differential equation and an initial condition satisfied by   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> is invested at <strong>A sum of   is invested at   interest. If   is the amount of the investment at time t for the case of continuous compounding, write a differential equation and an initial condition satisfied by   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> interest. If <strong>A sum of   is invested at   interest. If   is the amount of the investment at time t for the case of continuous compounding, write a differential equation and an initial condition satisfied by   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> is the amount of the investment at time t for the case of continuous compounding, write a differential equation and an initial condition satisfied by <strong>A sum of   is invested at   interest. If   is the amount of the investment at time t for the case of continuous compounding, write a differential equation and an initial condition satisfied by   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> .

A) <strong>A sum of   is invested at   interest. If   is the amount of the investment at time t for the case of continuous compounding, write a differential equation and an initial condition satisfied by   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>A sum of   is invested at   interest. If   is the amount of the investment at time t for the case of continuous compounding, write a differential equation and an initial condition satisfied by   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>A sum of   is invested at   interest. If   is the amount of the investment at time t for the case of continuous compounding, write a differential equation and an initial condition satisfied by   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>A sum of   is invested at   interest. If   is the amount of the investment at time t for the case of continuous compounding, write a differential equation and an initial condition satisfied by   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>A sum of   is invested at   interest. If   is the amount of the investment at time t for the case of continuous compounding, write a differential equation and an initial condition satisfied by   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
Suppose that a population develops according to the logistic equation <strong>Suppose that a population develops according to the logistic equation   , where t is measured in weeks. What is the carrying capacity?</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> , where t is measured in weeks. What is the carrying capacity?

A) <strong>Suppose that a population develops according to the logistic equation   , where t is measured in weeks. What is the carrying capacity?</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Suppose that a population develops according to the logistic equation   , where t is measured in weeks. What is the carrying capacity?</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Suppose that a population develops according to the logistic equation   , where t is measured in weeks. What is the carrying capacity?</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Suppose that a population develops according to the logistic equation   , where t is measured in weeks. What is the carrying capacity?</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Suppose that a population develops according to the logistic equation   , where t is measured in weeks. What is the carrying capacity?</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
One model for the spread of an epidemic is that the rate of spread is jointly proportional to the number of infected people and the number of uninfected people. In an isolated town of One model for the spread of an epidemic is that the rate of spread is jointly proportional to the number of infected people and the number of uninfected people. In an isolated town of   inhabitants,   people have a disease at the beginning of the week and   have it at the end of the week. How long does it take for   of the population to be infected?<div style=padding-top: 35px> inhabitants, One model for the spread of an epidemic is that the rate of spread is jointly proportional to the number of infected people and the number of uninfected people. In an isolated town of   inhabitants,   people have a disease at the beginning of the week and   have it at the end of the week. How long does it take for   of the population to be infected?<div style=padding-top: 35px> people have a disease at the beginning of the week and One model for the spread of an epidemic is that the rate of spread is jointly proportional to the number of infected people and the number of uninfected people. In an isolated town of   inhabitants,   people have a disease at the beginning of the week and   have it at the end of the week. How long does it take for   of the population to be infected?<div style=padding-top: 35px> have it at the end of the week. How long does it take for One model for the spread of an epidemic is that the rate of spread is jointly proportional to the number of infected people and the number of uninfected people. In an isolated town of   inhabitants,   people have a disease at the beginning of the week and   have it at the end of the week. How long does it take for   of the population to be infected?<div style=padding-top: 35px> of the population to be infected?
سؤال
A common inhabitant of human intestines is the bacterium Escherichia coli. A cell of this bacterium in a nutrient-broth medium divides into two cells every <strong>A common inhabitant of human intestines is the bacterium Escherichia coli. A cell of this bacterium in a nutrient-broth medium divides into two cells every   . The initial population of a culture is   cells. Find the number of cells after   hours.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> . The initial population of a culture is <strong>A common inhabitant of human intestines is the bacterium Escherichia coli. A cell of this bacterium in a nutrient-broth medium divides into two cells every   . The initial population of a culture is   cells. Find the number of cells after   hours.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> cells. Find the number of cells after <strong>A common inhabitant of human intestines is the bacterium Escherichia coli. A cell of this bacterium in a nutrient-broth medium divides into two cells every   . The initial population of a culture is   cells. Find the number of cells after   hours.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> hours.

A) <strong>A common inhabitant of human intestines is the bacterium Escherichia coli. A cell of this bacterium in a nutrient-broth medium divides into two cells every   . The initial population of a culture is   cells. Find the number of cells after   hours.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>A common inhabitant of human intestines is the bacterium Escherichia coli. A cell of this bacterium in a nutrient-broth medium divides into two cells every   . The initial population of a culture is   cells. Find the number of cells after   hours.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>A common inhabitant of human intestines is the bacterium Escherichia coli. A cell of this bacterium in a nutrient-broth medium divides into two cells every   . The initial population of a culture is   cells. Find the number of cells after   hours.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>A common inhabitant of human intestines is the bacterium Escherichia coli. A cell of this bacterium in a nutrient-broth medium divides into two cells every   . The initial population of a culture is   cells. Find the number of cells after   hours.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>A common inhabitant of human intestines is the bacterium Escherichia coli. A cell of this bacterium in a nutrient-broth medium divides into two cells every   . The initial population of a culture is   cells. Find the number of cells after   hours.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
Solve the differential equation. <strong>Solve the differential equation.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>

A) <strong>Solve the differential equation.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Solve the differential equation.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Solve the differential equation.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Solve the differential equation.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Solve the differential equation.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
Experiments show that if the chemical reaction Experiments show that if the chemical reaction   takes place at   , the rate of reaction of dinitrogen pentoxide is proportional to its concentration as follows :   How long will the reaction take to reduce the concentration of   to 50% of its original value?<div style=padding-top: 35px> takes place at Experiments show that if the chemical reaction   takes place at   , the rate of reaction of dinitrogen pentoxide is proportional to its concentration as follows :   How long will the reaction take to reduce the concentration of   to 50% of its original value?<div style=padding-top: 35px> , the rate of reaction of dinitrogen pentoxide is proportional to its concentration as follows : Experiments show that if the chemical reaction   takes place at   , the rate of reaction of dinitrogen pentoxide is proportional to its concentration as follows :   How long will the reaction take to reduce the concentration of   to 50% of its original value?<div style=padding-top: 35px> How long will the reaction take to reduce the concentration of Experiments show that if the chemical reaction   takes place at   , the rate of reaction of dinitrogen pentoxide is proportional to its concentration as follows :   How long will the reaction take to reduce the concentration of   to 50% of its original value?<div style=padding-top: 35px> to 50% of its original value?
سؤال
Solve the differential equation. Solve the differential equation.  <div style=padding-top: 35px>
سؤال
A certain small country has $20 billion in paper currency in circulation, and each day $70 million comes into the country's banks. The government decides to introduce new currency by having the banks replace old bills with new ones whenever old currency comes into the banks. Let A certain small country has $20 billion in paper currency in circulation, and each day $70 million comes into the country's banks. The government decides to introduce new currency by having the banks replace old bills with new ones whenever old currency comes into the banks. Let   denote the amount of new currency in circulation at time t with   . Formulate and solve a mathematical model in the form of an initial-value problem that represents the flow of the new currency into circulation (in billions per day).<div style=padding-top: 35px> denote the amount of new currency in circulation at time t with A certain small country has $20 billion in paper currency in circulation, and each day $70 million comes into the country's banks. The government decides to introduce new currency by having the banks replace old bills with new ones whenever old currency comes into the banks. Let   denote the amount of new currency in circulation at time t with   . Formulate and solve a mathematical model in the form of an initial-value problem that represents the flow of the new currency into circulation (in billions per day).<div style=padding-top: 35px> . Formulate and solve a mathematical model in the form of an initial-value problem that represents the "flow" of the new currency into circulation (in billions per day).
سؤال
Solve the differential equation. Solve the differential equation.  <div style=padding-top: 35px>
سؤال
Find the solution of the differential equation that satisfies the initial condition Find the solution of the differential equation that satisfies the initial condition   .  <div style=padding-top: 35px> . Find the solution of the differential equation that satisfies the initial condition   .  <div style=padding-top: 35px>
سؤال
Find the orthogonal trajectories of the family of curves. <strong>Find the orthogonal trajectories of the family of curves.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>

A) <strong>Find the orthogonal trajectories of the family of curves.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Find the orthogonal trajectories of the family of curves.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Find the orthogonal trajectories of the family of curves.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Find the orthogonal trajectories of the family of curves.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Find the orthogonal trajectories of the family of curves.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
Select a direction field for the differential equation Select a direction field for the differential equation   from a set of direction fields labeled I-IV.  <div style=padding-top: 35px> from a set of direction fields labeled I-IV. Select a direction field for the differential equation   from a set of direction fields labeled I-IV.  <div style=padding-top: 35px>
سؤال
A population is modeled by the differential equation. <strong>A population is modeled by the differential equation.   For what values of P is the population increasing?</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> For what values of P is the population increasing?

A) <strong>A population is modeled by the differential equation.   For what values of P is the population increasing?</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>A population is modeled by the differential equation.   For what values of P is the population increasing?</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>A population is modeled by the differential equation.   For what values of P is the population increasing?</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>A population is modeled by the differential equation.   For what values of P is the population increasing?</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>A population is modeled by the differential equation.   For what values of P is the population increasing?</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
Choose the differential equation corresponding to this direction field. <strong>Choose the differential equation corresponding to this direction field.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>

A) <strong>Choose the differential equation corresponding to this direction field.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Choose the differential equation corresponding to this direction field.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Choose the differential equation corresponding to this direction field.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Choose the differential equation corresponding to this direction field.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Choose the differential equation corresponding to this direction field.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
Find the orthogonal trajectories of the family of curves. Find the orthogonal trajectories of the family of curves.  <div style=padding-top: 35px>
سؤال
Solve the differential equation. Solve the differential equation.  <div style=padding-top: 35px>
سؤال
A tank contains A tank contains   L of brine with   kg of dissolved salt. Pure water enters the tank at a rate of   L/min. The solution is kept thoroughly mixed and drains from the tank at the same rate. How much salt is in the tank after   minutes?<div style=padding-top: 35px> L of brine with A tank contains   L of brine with   kg of dissolved salt. Pure water enters the tank at a rate of   L/min. The solution is kept thoroughly mixed and drains from the tank at the same rate. How much salt is in the tank after   minutes?<div style=padding-top: 35px> kg of dissolved salt. Pure water enters the tank at a rate of A tank contains   L of brine with   kg of dissolved salt. Pure water enters the tank at a rate of   L/min. The solution is kept thoroughly mixed and drains from the tank at the same rate. How much salt is in the tank after   minutes?<div style=padding-top: 35px> L/min. The solution is kept thoroughly mixed and drains from the tank at the same rate. How much salt is in the tank after A tank contains   L of brine with   kg of dissolved salt. Pure water enters the tank at a rate of   L/min. The solution is kept thoroughly mixed and drains from the tank at the same rate. How much salt is in the tank after   minutes?<div style=padding-top: 35px> minutes?
سؤال
Which equation does the function <strong>Which equation does the function   satisfy?</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> satisfy?

A) <strong>Which equation does the function   satisfy?</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Which equation does the function   satisfy?</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Which equation does the function   satisfy?</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Which equation does the function   satisfy?</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Which equation does the function   satisfy?</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
Solve the initial-value problem. <strong>Solve the initial-value problem.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>

A) <strong>Solve the initial-value problem.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Solve the initial-value problem.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Solve the initial-value problem.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Solve the initial-value problem.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Solve the initial-value problem.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
Find the solution of the differential equation Find the solution of the differential equation   that satisfies the initial condition   .<div style=padding-top: 35px> that satisfies the initial condition Find the solution of the differential equation   that satisfies the initial condition   .<div style=padding-top: 35px> .
سؤال
Use Euler's method with step size 0.1 to estimate Use Euler's method with step size 0.1 to estimate   , where   is the solution of the initial-value problem. Round your answer to four decimal places.  <div style=padding-top: 35px> , where Use Euler's method with step size 0.1 to estimate   , where   is the solution of the initial-value problem. Round your answer to four decimal places.  <div style=padding-top: 35px> is the solution of the initial-value problem. Round your answer to four decimal places. Use Euler's method with step size 0.1 to estimate   , where   is the solution of the initial-value problem. Round your answer to four decimal places.  <div style=padding-top: 35px>
سؤال
Use Euler's method with step size 0.25 to estimate <strong>Use Euler's method with step size 0.25 to estimate   , where   is the solution of the initial-value problem. Round your answer to four decimal places.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> , where <strong>Use Euler's method with step size 0.25 to estimate   , where   is the solution of the initial-value problem. Round your answer to four decimal places.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> is the solution of the initial-value problem. Round your answer to four decimal places. <strong>Use Euler's method with step size 0.25 to estimate   , where   is the solution of the initial-value problem. Round your answer to four decimal places.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>

A) <strong>Use Euler's method with step size 0.25 to estimate   , where   is the solution of the initial-value problem. Round your answer to four decimal places.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Use Euler's method with step size 0.25 to estimate   , where   is the solution of the initial-value problem. Round your answer to four decimal places.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Use Euler's method with step size 0.25 to estimate   , where   is the solution of the initial-value problem. Round your answer to four decimal places.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Use Euler's method with step size 0.25 to estimate   , where   is the solution of the initial-value problem. Round your answer to four decimal places.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Use Euler's method with step size 0.25 to estimate   , where   is the solution of the initial-value problem. Round your answer to four decimal places.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
Solve the differential equation. <strong>Solve the differential equation.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>

A) <strong>Solve the differential equation.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Solve the differential equation.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Solve the differential equation.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Solve the differential equation.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Solve the differential equation.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
The solution of the differential equation The solution of the differential equation   satisfies the initial condition   . Find the limit.  <div style=padding-top: 35px> satisfies the initial condition The solution of the differential equation   satisfies the initial condition   . Find the limit.  <div style=padding-top: 35px> .
Find the limit. The solution of the differential equation   satisfies the initial condition   . Find the limit.  <div style=padding-top: 35px>
سؤال
Kirchhoff's Law gives us the derivative equation Kirchhoff's Law gives us the derivative equation   . If   , use Euler's method with step size 0.1 to estimate   after 0.3 second.<div style=padding-top: 35px> .
If Kirchhoff's Law gives us the derivative equation   . If   , use Euler's method with step size 0.1 to estimate   after 0.3 second.<div style=padding-top: 35px> , use Euler's method with step size 0.1 to estimate Kirchhoff's Law gives us the derivative equation   . If   , use Euler's method with step size 0.1 to estimate   after 0.3 second.<div style=padding-top: 35px> after 0.3 second.
سؤال
For what nonzero values of k does the function <strong>For what nonzero values of k does the function   satisfy the differential equation   for all values of A and B? </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> satisfy the differential equation <strong>For what nonzero values of k does the function   satisfy the differential equation   for all values of A and B? </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> for all values of A and B?

A) <strong>For what nonzero values of k does the function   satisfy the differential equation   for all values of A and B? </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>For what nonzero values of k does the function   satisfy the differential equation   for all values of A and B? </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>For what nonzero values of k does the function   satisfy the differential equation   for all values of A and B? </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>For what nonzero values of k does the function   satisfy the differential equation   for all values of A and B? </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>For what nonzero values of k does the function   satisfy the differential equation   for all values of A and B? </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
For what values of k does the function <strong>For what values of k does the function   satisfy the differential equation   ? </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> satisfy the differential equation <strong>For what values of k does the function   satisfy the differential equation   ? </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> ?

A) <strong>For what values of k does the function   satisfy the differential equation   ? </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>For what values of k does the function   satisfy the differential equation   ? </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>For what values of k does the function   satisfy the differential equation   ? </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>For what values of k does the function   satisfy the differential equation   ? </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>For what values of k does the function   satisfy the differential equation   ? </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
Newton's Law of Cooling states that the rate of cooling of an object is proportional to the temperature difference between the object and its surroundings. Suppose that a roast turkey is taken from an oven when its temperature has reached <strong>Newton's Law of Cooling states that the rate of cooling of an object is proportional to the temperature difference between the object and its surroundings. Suppose that a roast turkey is taken from an oven when its temperature has reached   and is placed on a table in a room where the temperature is   . If   is the temperature of the turkey after t minutes, then Newton's Law of Cooling implies that   . This could be solved as a separable differential equation. Another method is to make the change of variable   . If the temperature of the turkey is   after half an hour, what is the temperature after 35 min?</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> and is placed on a table in a room where the temperature is <strong>Newton's Law of Cooling states that the rate of cooling of an object is proportional to the temperature difference between the object and its surroundings. Suppose that a roast turkey is taken from an oven when its temperature has reached   and is placed on a table in a room where the temperature is   . If   is the temperature of the turkey after t minutes, then Newton's Law of Cooling implies that   . This could be solved as a separable differential equation. Another method is to make the change of variable   . If the temperature of the turkey is   after half an hour, what is the temperature after 35 min?</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> . If <strong>Newton's Law of Cooling states that the rate of cooling of an object is proportional to the temperature difference between the object and its surroundings. Suppose that a roast turkey is taken from an oven when its temperature has reached   and is placed on a table in a room where the temperature is   . If   is the temperature of the turkey after t minutes, then Newton's Law of Cooling implies that   . This could be solved as a separable differential equation. Another method is to make the change of variable   . If the temperature of the turkey is   after half an hour, what is the temperature after 35 min?</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> is the temperature of the turkey after t minutes, then Newton's Law of Cooling implies that <strong>Newton's Law of Cooling states that the rate of cooling of an object is proportional to the temperature difference between the object and its surroundings. Suppose that a roast turkey is taken from an oven when its temperature has reached   and is placed on a table in a room where the temperature is   . If   is the temperature of the turkey after t minutes, then Newton's Law of Cooling implies that   . This could be solved as a separable differential equation. Another method is to make the change of variable   . If the temperature of the turkey is   after half an hour, what is the temperature after 35 min?</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> . This could be solved as a separable differential equation. Another method is to make the change of variable <strong>Newton's Law of Cooling states that the rate of cooling of an object is proportional to the temperature difference between the object and its surroundings. Suppose that a roast turkey is taken from an oven when its temperature has reached   and is placed on a table in a room where the temperature is   . If   is the temperature of the turkey after t minutes, then Newton's Law of Cooling implies that   . This could be solved as a separable differential equation. Another method is to make the change of variable   . If the temperature of the turkey is   after half an hour, what is the temperature after 35 min?</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> . If the temperature of the turkey is <strong>Newton's Law of Cooling states that the rate of cooling of an object is proportional to the temperature difference between the object and its surroundings. Suppose that a roast turkey is taken from an oven when its temperature has reached   and is placed on a table in a room where the temperature is   . If   is the temperature of the turkey after t minutes, then Newton's Law of Cooling implies that   . This could be solved as a separable differential equation. Another method is to make the change of variable   . If the temperature of the turkey is   after half an hour, what is the temperature after 35 min?</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> after half an hour, what is the temperature after 35 min?

A) <strong>Newton's Law of Cooling states that the rate of cooling of an object is proportional to the temperature difference between the object and its surroundings. Suppose that a roast turkey is taken from an oven when its temperature has reached   and is placed on a table in a room where the temperature is   . If   is the temperature of the turkey after t minutes, then Newton's Law of Cooling implies that   . This could be solved as a separable differential equation. Another method is to make the change of variable   . If the temperature of the turkey is   after half an hour, what is the temperature after 35 min?</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Newton's Law of Cooling states that the rate of cooling of an object is proportional to the temperature difference between the object and its surroundings. Suppose that a roast turkey is taken from an oven when its temperature has reached   and is placed on a table in a room where the temperature is   . If   is the temperature of the turkey after t minutes, then Newton's Law of Cooling implies that   . This could be solved as a separable differential equation. Another method is to make the change of variable   . If the temperature of the turkey is   after half an hour, what is the temperature after 35 min?</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Newton's Law of Cooling states that the rate of cooling of an object is proportional to the temperature difference between the object and its surroundings. Suppose that a roast turkey is taken from an oven when its temperature has reached   and is placed on a table in a room where the temperature is   . If   is the temperature of the turkey after t minutes, then Newton's Law of Cooling implies that   . This could be solved as a separable differential equation. Another method is to make the change of variable   . If the temperature of the turkey is   after half an hour, what is the temperature after 35 min?</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Newton's Law of Cooling states that the rate of cooling of an object is proportional to the temperature difference between the object and its surroundings. Suppose that a roast turkey is taken from an oven when its temperature has reached   and is placed on a table in a room where the temperature is   . If   is the temperature of the turkey after t minutes, then Newton's Law of Cooling implies that   . This could be solved as a separable differential equation. Another method is to make the change of variable   . If the temperature of the turkey is   after half an hour, what is the temperature after 35 min?</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Newton's Law of Cooling states that the rate of cooling of an object is proportional to the temperature difference between the object and its surroundings. Suppose that a roast turkey is taken from an oven when its temperature has reached   and is placed on a table in a room where the temperature is   . If   is the temperature of the turkey after t minutes, then Newton's Law of Cooling implies that   . This could be solved as a separable differential equation. Another method is to make the change of variable   . If the temperature of the turkey is   after half an hour, what is the temperature after 35 min?</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
A population is modeled by the differential equation A population is modeled by the differential equation   . For what values of P is the population decreasing?<div style=padding-top: 35px> .
For what values of P is the population decreasing?
سؤال
Which of the following functions are the constant solutions of the equation Which of the following functions are the constant solutions of the equation   a.   b.   c.   d.   e.  <div style=padding-top: 35px>
a. Which of the following functions are the constant solutions of the equation   a.   b.   c.   d.   e.  <div style=padding-top: 35px>
b. Which of the following functions are the constant solutions of the equation   a.   b.   c.   d.   e.  <div style=padding-top: 35px>
c. Which of the following functions are the constant solutions of the equation   a.   b.   c.   d.   e.  <div style=padding-top: 35px>
d. Which of the following functions are the constant solutions of the equation   a.   b.   c.   d.   e.  <div style=padding-top: 35px>
e. Which of the following functions are the constant solutions of the equation   a.   b.   c.   d.   e.  <div style=padding-top: 35px>
سؤال
A sum of A sum of   is invested at   interest. If   is the amount of the investment at time t for the case of continuous compounding, write a differential equation and an initial condition satisfied by   .<div style=padding-top: 35px> is invested at A sum of   is invested at   interest. If   is the amount of the investment at time t for the case of continuous compounding, write a differential equation and an initial condition satisfied by   .<div style=padding-top: 35px> interest. If A sum of   is invested at   interest. If   is the amount of the investment at time t for the case of continuous compounding, write a differential equation and an initial condition satisfied by   .<div style=padding-top: 35px> is the amount of the investment at time t for the case of continuous compounding, write a differential equation and an initial condition satisfied by A sum of   is invested at   interest. If   is the amount of the investment at time t for the case of continuous compounding, write a differential equation and an initial condition satisfied by   .<div style=padding-top: 35px> .
سؤال
A function A function   satisfies the differential equation   . What are the constant solutions of the equation?<div style=padding-top: 35px> satisfies the differential equation A function   satisfies the differential equation   . What are the constant solutions of the equation?<div style=padding-top: 35px> .
What are the constant solutions of the equation?
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Deck 9: Differential Equations
1
Solve the initial-value problem. <strong>Solve the initial-value problem.  </strong> A)   B)   C)   D)   E)

A) <strong>Solve the initial-value problem.  </strong> A)   B)   C)   D)   E)
B) <strong>Solve the initial-value problem.  </strong> A)   B)   C)   D)   E)
C) <strong>Solve the initial-value problem.  </strong> A)   B)   C)   D)   E)
D) <strong>Solve the initial-value problem.  </strong> A)   B)   C)   D)   E)
E) <strong>Solve the initial-value problem.  </strong> A)   B)   C)   D)   E)
2
Solve the differential equation. <strong>Solve the differential equation.  </strong> A)   B)   C)   D)   E)

A) <strong>Solve the differential equation.  </strong> A)   B)   C)   D)   E)
B) <strong>Solve the differential equation.  </strong> A)   B)   C)   D)   E)
C) <strong>Solve the differential equation.  </strong> A)   B)   C)   D)   E)
D) <strong>Solve the differential equation.  </strong> A)   B)   C)   D)   E)
E) <strong>Solve the differential equation.  </strong> A)   B)   C)   D)   E)
3
Solve the initial-value problem. <strong>Solve the initial-value problem.  </strong> A)   B)   C)   D)   E)

A) <strong>Solve the initial-value problem.  </strong> A)   B)   C)   D)   E)
B) <strong>Solve the initial-value problem.  </strong> A)   B)   C)   D)   E)
C) <strong>Solve the initial-value problem.  </strong> A)   B)   C)   D)   E)
D) <strong>Solve the initial-value problem.  </strong> A)   B)   C)   D)   E)
E) <strong>Solve the initial-value problem.  </strong> A)   B)   C)   D)   E)
4
Determine whether the differential equation is linear. <strong>Determine whether the differential equation is linear.  </strong> A)the equation is not linear B)the equation is linear

A)the equation is not linear
B)the equation is linear
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Solve the differential equation. <strong>Solve the differential equation.  </strong> A)   B)   C)   D)   E)

A) <strong>Solve the differential equation.  </strong> A)   B)   C)   D)   E)
B) <strong>Solve the differential equation.  </strong> A)   B)   C)   D)   E)
C) <strong>Solve the differential equation.  </strong> A)   B)   C)   D)   E)
D) <strong>Solve the differential equation.  </strong> A)   B)   C)   D)   E)
E) <strong>Solve the differential equation.  </strong> A)   B)   C)   D)   E)
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6
In the circuit shown in Figure, a generator supplies a voltage of <strong>In the circuit shown in Figure, a generator supplies a voltage of   volts, the inductance is 2 H, the resistance is 40   , and   . Find the current 0.2 s after the switch is closed. Round your answer to two decimal places.  </strong> A) 0.75 A B)   C)   D)   E)   volts, the inductance is 2 H, the resistance is 40 <strong>In the circuit shown in Figure, a generator supplies a voltage of   volts, the inductance is 2 H, the resistance is 40   , and   . Find the current 0.2 s after the switch is closed. Round your answer to two decimal places.  </strong> A) 0.75 A B)   C)   D)   E)   , and <strong>In the circuit shown in Figure, a generator supplies a voltage of   volts, the inductance is 2 H, the resistance is 40   , and   . Find the current 0.2 s after the switch is closed. Round your answer to two decimal places.  </strong> A) 0.75 A B)   C)   D)   E)   . Find the current 0.2 s after the switch is closed. Round your answer to two decimal places. <strong>In the circuit shown in Figure, a generator supplies a voltage of   volts, the inductance is 2 H, the resistance is 40   , and   . Find the current 0.2 s after the switch is closed. Round your answer to two decimal places.  </strong> A) 0.75 A B)   C)   D)   E)

A) 0.75 A
B) <strong>In the circuit shown in Figure, a generator supplies a voltage of   volts, the inductance is 2 H, the resistance is 40   , and   . Find the current 0.2 s after the switch is closed. Round your answer to two decimal places.  </strong> A) 0.75 A B)   C)   D)   E)
C) <strong>In the circuit shown in Figure, a generator supplies a voltage of   volts, the inductance is 2 H, the resistance is 40   , and   . Find the current 0.2 s after the switch is closed. Round your answer to two decimal places.  </strong> A) 0.75 A B)   C)   D)   E)
D) <strong>In the circuit shown in Figure, a generator supplies a voltage of   volts, the inductance is 2 H, the resistance is 40   , and   . Find the current 0.2 s after the switch is closed. Round your answer to two decimal places.  </strong> A) 0.75 A B)   C)   D)   E)
E) <strong>In the circuit shown in Figure, a generator supplies a voltage of   volts, the inductance is 2 H, the resistance is 40   , and   . Find the current 0.2 s after the switch is closed. Round your answer to two decimal places.  </strong> A) 0.75 A B)   C)   D)   E)
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7
An object with mass m is dropped from rest and we assume that the air resistance is proportional to the speed of the object. If An object with mass m is dropped from rest and we assume that the air resistance is proportional to the speed of the object. If   is the distance dropped after t seconds, then the speed is   and the acceleration is   . If g is the acceleration due to gravity, then the downward force on the object is   , where c is a positive constant, and Newton's Second Law gives   . Find the limiting velocity. is the distance dropped after t seconds, then the speed is An object with mass m is dropped from rest and we assume that the air resistance is proportional to the speed of the object. If   is the distance dropped after t seconds, then the speed is   and the acceleration is   . If g is the acceleration due to gravity, then the downward force on the object is   , where c is a positive constant, and Newton's Second Law gives   . Find the limiting velocity. and the acceleration is An object with mass m is dropped from rest and we assume that the air resistance is proportional to the speed of the object. If   is the distance dropped after t seconds, then the speed is   and the acceleration is   . If g is the acceleration due to gravity, then the downward force on the object is   , where c is a positive constant, and Newton's Second Law gives   . Find the limiting velocity. . If g is the acceleration due to gravity, then the downward force on the object is An object with mass m is dropped from rest and we assume that the air resistance is proportional to the speed of the object. If   is the distance dropped after t seconds, then the speed is   and the acceleration is   . If g is the acceleration due to gravity, then the downward force on the object is   , where c is a positive constant, and Newton's Second Law gives   . Find the limiting velocity. , where c is a positive constant, and Newton's Second Law gives An object with mass m is dropped from rest and we assume that the air resistance is proportional to the speed of the object. If   is the distance dropped after t seconds, then the speed is   and the acceleration is   . If g is the acceleration due to gravity, then the downward force on the object is   , where c is a positive constant, and Newton's Second Law gives   . Find the limiting velocity. .
Find the limiting velocity.
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8
Solve the initial-value problem. <strong>Solve the initial-value problem.  </strong> A)   B)   C)   D)   E)

A) <strong>Solve the initial-value problem.  </strong> A)   B)   C)   D)   E)
B) <strong>Solve the initial-value problem.  </strong> A)   B)   C)   D)   E)
C) <strong>Solve the initial-value problem.  </strong> A)   B)   C)   D)   E)
D) <strong>Solve the initial-value problem.  </strong> A)   B)   C)   D)   E)
E) <strong>Solve the initial-value problem.  </strong> A)   B)   C)   D)   E)
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9
We modeled populations of aphids and ladybugs with a Lotka-Volterra system. Suppose we modify those equations as follows: <strong>We modeled populations of aphids and ladybugs with a Lotka-Volterra system. Suppose we modify those equations as follows:   ,  </strong> A)   B)   C)   D)   E)   , <strong>We modeled populations of aphids and ladybugs with a Lotka-Volterra system. Suppose we modify those equations as follows:   ,  </strong> A)   B)   C)   D)   E)

A) <strong>We modeled populations of aphids and ladybugs with a Lotka-Volterra system. Suppose we modify those equations as follows:   ,  </strong> A)   B)   C)   D)   E)
B) <strong>We modeled populations of aphids and ladybugs with a Lotka-Volterra system. Suppose we modify those equations as follows:   ,  </strong> A)   B)   C)   D)   E)
C) <strong>We modeled populations of aphids and ladybugs with a Lotka-Volterra system. Suppose we modify those equations as follows:   ,  </strong> A)   B)   C)   D)   E)
D) <strong>We modeled populations of aphids and ladybugs with a Lotka-Volterra system. Suppose we modify those equations as follows:   ,  </strong> A)   B)   C)   D)   E)
E) <strong>We modeled populations of aphids and ladybugs with a Lotka-Volterra system. Suppose we modify those equations as follows:   ,  </strong> A)   B)   C)   D)   E)
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10
A phase trajectory is shown for populations of rabbits <strong>A phase trajectory is shown for populations of rabbits   and foxes   . Describe how each population changes as time goes by.   Select the correct statement.</strong> A)At   the population of foxes reaches a minimum of about 30. B)At   the number of rabbits rebounds to 500. C)At   the number of foxes reaches a maximum of about 2400. and foxes <strong>A phase trajectory is shown for populations of rabbits   and foxes   . Describe how each population changes as time goes by.   Select the correct statement.</strong> A)At   the population of foxes reaches a minimum of about 30. B)At   the number of rabbits rebounds to 500. C)At   the number of foxes reaches a maximum of about 2400. . Describe how each population changes as time goes by. <strong>A phase trajectory is shown for populations of rabbits   and foxes   . Describe how each population changes as time goes by.   Select the correct statement.</strong> A)At   the population of foxes reaches a minimum of about 30. B)At   the number of rabbits rebounds to 500. C)At   the number of foxes reaches a maximum of about 2400. Select the correct statement.

A)At <strong>A phase trajectory is shown for populations of rabbits   and foxes   . Describe how each population changes as time goes by.   Select the correct statement.</strong> A)At   the population of foxes reaches a minimum of about 30. B)At   the number of rabbits rebounds to 500. C)At   the number of foxes reaches a maximum of about 2400. the population of foxes reaches a minimum of about 30.
B)At <strong>A phase trajectory is shown for populations of rabbits   and foxes   . Describe how each population changes as time goes by.   Select the correct statement.</strong> A)At   the population of foxes reaches a minimum of about 30. B)At   the number of rabbits rebounds to 500. C)At   the number of foxes reaches a maximum of about 2400. the number of rabbits rebounds to 500.
C)At <strong>A phase trajectory is shown for populations of rabbits   and foxes   . Describe how each population changes as time goes by.   Select the correct statement.</strong> A)At   the population of foxes reaches a minimum of about 30. B)At   the number of rabbits rebounds to 500. C)At   the number of foxes reaches a maximum of about 2400. the number of foxes reaches a maximum of about 2400.
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11
Which of the following functions is a solution of the differential equation? <strong>Which of the following functions is a solution of the differential equation?   </strong> A)   B)   C)   D)   E)

A) <strong>Which of the following functions is a solution of the differential equation?   </strong> A)   B)   C)   D)   E)
B) <strong>Which of the following functions is a solution of the differential equation?   </strong> A)   B)   C)   D)   E)
C) <strong>Which of the following functions is a solution of the differential equation?   </strong> A)   B)   C)   D)   E)
D) <strong>Which of the following functions is a solution of the differential equation?   </strong> A)   B)   C)   D)   E)
E) <strong>Which of the following functions is a solution of the differential equation?   </strong> A)   B)   C)   D)   E)
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12
Solve the differential equation. <strong>Solve the differential equation.  </strong> A)   B)   C)   D)   E)

A) <strong>Solve the differential equation.  </strong> A)   B)   C)   D)   E)
B) <strong>Solve the differential equation.  </strong> A)   B)   C)   D)   E)
C) <strong>Solve the differential equation.  </strong> A)   B)   C)   D)   E)
D) <strong>Solve the differential equation.  </strong> A)   B)   C)   D)   E)
E) <strong>Solve the differential equation.  </strong> A)   B)   C)   D)   E)
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13
Solve the differential equation. Solve the differential equation.
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14
Determine whether the differential equation is linear. Determine whether the differential equation is linear.
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15
Solve the initial-value problem. <strong>Solve the initial-value problem.  </strong> A)   B)   C)   D)   E)

A) <strong>Solve the initial-value problem.  </strong> A)   B)   C)   D)   E)
B) <strong>Solve the initial-value problem.  </strong> A)   B)   C)   D)   E)
C) <strong>Solve the initial-value problem.  </strong> A)   B)   C)   D)   E)
D) <strong>Solve the initial-value problem.  </strong> A)   B)   C)   D)   E)
E) <strong>Solve the initial-value problem.  </strong> A)   B)   C)   D)   E)
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16
Solve the initial-value problem. Solve the initial-value problem.
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17
Solve the initial-value problem. Solve the initial-value problem.
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18
Find the solution of the initial-value problem and use it to find the population when Find the solution of the initial-value problem and use it to find the population when   .  . Find the solution of the initial-value problem and use it to find the population when   .
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19
Let <strong>Let   be the performance level of someone learning a skill as a function of the training time t. The graph of P is called a learning curve. We propose the differential equation   as a reasonable model for learning, where r is a positive constant. Solve it as a linear differential equation.</strong> A)   B)   C)   D)   E)   be the performance level of someone learning a skill as a function of the training time t. The graph of P is called a learning curve. We propose the differential equation <strong>Let   be the performance level of someone learning a skill as a function of the training time t. The graph of P is called a learning curve. We propose the differential equation   as a reasonable model for learning, where r is a positive constant. Solve it as a linear differential equation.</strong> A)   B)   C)   D)   E)   as a reasonable model for learning, where r is a positive constant. Solve it as a linear differential equation.

A) <strong>Let   be the performance level of someone learning a skill as a function of the training time t. The graph of P is called a learning curve. We propose the differential equation   as a reasonable model for learning, where r is a positive constant. Solve it as a linear differential equation.</strong> A)   B)   C)   D)   E)
B) <strong>Let   be the performance level of someone learning a skill as a function of the training time t. The graph of P is called a learning curve. We propose the differential equation   as a reasonable model for learning, where r is a positive constant. Solve it as a linear differential equation.</strong> A)   B)   C)   D)   E)
C) <strong>Let   be the performance level of someone learning a skill as a function of the training time t. The graph of P is called a learning curve. We propose the differential equation   as a reasonable model for learning, where r is a positive constant. Solve it as a linear differential equation.</strong> A)   B)   C)   D)   E)
D) <strong>Let   be the performance level of someone learning a skill as a function of the training time t. The graph of P is called a learning curve. We propose the differential equation   as a reasonable model for learning, where r is a positive constant. Solve it as a linear differential equation.</strong> A)   B)   C)   D)   E)
E) <strong>Let   be the performance level of someone learning a skill as a function of the training time t. The graph of P is called a learning curve. We propose the differential equation   as a reasonable model for learning, where r is a positive constant. Solve it as a linear differential equation.</strong> A)   B)   C)   D)   E)
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20
Solve the initial-value problem. Solve the initial-value problem.
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21
Suppose that a population grows according to a logistic model with carrying capacity <strong>Suppose that a population grows according to a logistic model with carrying capacity   and   per year. Choose the logistic differential equation for these data.</strong> A)   B)   C)   D)   E)   and <strong>Suppose that a population grows according to a logistic model with carrying capacity   and   per year. Choose the logistic differential equation for these data.</strong> A)   B)   C)   D)   E)   per year. Choose the logistic differential equation for these data.

A) <strong>Suppose that a population grows according to a logistic model with carrying capacity   and   per year. Choose the logistic differential equation for these data.</strong> A)   B)   C)   D)   E)
B) <strong>Suppose that a population grows according to a logistic model with carrying capacity   and   per year. Choose the logistic differential equation for these data.</strong> A)   B)   C)   D)   E)
C) <strong>Suppose that a population grows according to a logistic model with carrying capacity   and   per year. Choose the logistic differential equation for these data.</strong> A)   B)   C)   D)   E)
D) <strong>Suppose that a population grows according to a logistic model with carrying capacity   and   per year. Choose the logistic differential equation for these data.</strong> A)   B)   C)   D)   E)
E) <strong>Suppose that a population grows according to a logistic model with carrying capacity   and   per year. Choose the logistic differential equation for these data.</strong> A)   B)   C)   D)   E)
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22
Let Let   . What are the equilibrium solutions? .
What are the equilibrium solutions?
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23
The population of the world was about 5.3 billion in 1990. Birth rates in the 1990s range from 35 to 40 million per year and death rates range from 15 to 20 million per year. Let's assume that the carrying capacity for world population is 100 billion. Use the logistic model to predict the world population in the 2,450 year. Calculate your answer in billions to one decimal place. (Because the initial population is small compared to the carrying capacity, you can take k to be an estimate of the initial relative growth rate.)

A)59.2 billion
B)32.9 billion
C)78.3 billion
D)17.1 billion
E)24.1 billion
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24
The rate of change of atmospheric pressure P with respect to altitude h is proportional to P provided that the temperature is constant. At The rate of change of atmospheric pressure P with respect to altitude h is proportional to P provided that the temperature is constant. At   the pressure is   at sea level and   at   . What is the pressure at an altitude of   ? the pressure is The rate of change of atmospheric pressure P with respect to altitude h is proportional to P provided that the temperature is constant. At   the pressure is   at sea level and   at   . What is the pressure at an altitude of   ? at sea level and The rate of change of atmospheric pressure P with respect to altitude h is proportional to P provided that the temperature is constant. At   the pressure is   at sea level and   at   . What is the pressure at an altitude of   ? at The rate of change of atmospheric pressure P with respect to altitude h is proportional to P provided that the temperature is constant. At   the pressure is   at sea level and   at   . What is the pressure at an altitude of   ? . What is the pressure at an altitude of The rate of change of atmospheric pressure P with respect to altitude h is proportional to P provided that the temperature is constant. At   the pressure is   at sea level and   at   . What is the pressure at an altitude of   ? ?
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25
Let c be a positive number. A differential equation of the form Let c be a positive number. A differential equation of the form   where k is a positive constant, is called a doomsday equation because the exponent in the expression   is larger than the exponent 1for natural growth. An especially prolific breed of rabbits has the growth term   . If   such rabbits breed initially and the warren has   rabbits after   months, then when is doomsday? where k is a positive constant, is called a doomsday equation because the exponent in the expression Let c be a positive number. A differential equation of the form   where k is a positive constant, is called a doomsday equation because the exponent in the expression   is larger than the exponent 1for natural growth. An especially prolific breed of rabbits has the growth term   . If   such rabbits breed initially and the warren has   rabbits after   months, then when is doomsday? is larger than the exponent 1for natural growth. An especially prolific breed of rabbits has the growth term Let c be a positive number. A differential equation of the form   where k is a positive constant, is called a doomsday equation because the exponent in the expression   is larger than the exponent 1for natural growth. An especially prolific breed of rabbits has the growth term   . If   such rabbits breed initially and the warren has   rabbits after   months, then when is doomsday? . If Let c be a positive number. A differential equation of the form   where k is a positive constant, is called a doomsday equation because the exponent in the expression   is larger than the exponent 1for natural growth. An especially prolific breed of rabbits has the growth term   . If   such rabbits breed initially and the warren has   rabbits after   months, then when is doomsday? such rabbits breed initially and the warren has Let c be a positive number. A differential equation of the form   where k is a positive constant, is called a doomsday equation because the exponent in the expression   is larger than the exponent 1for natural growth. An especially prolific breed of rabbits has the growth term   . If   such rabbits breed initially and the warren has   rabbits after   months, then when is doomsday? rabbits after Let c be a positive number. A differential equation of the form   where k is a positive constant, is called a doomsday equation because the exponent in the expression   is larger than the exponent 1for natural growth. An especially prolific breed of rabbits has the growth term   . If   such rabbits breed initially and the warren has   rabbits after   months, then when is doomsday? months, then when is doomsday?
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26
Consider the differential equation Consider the differential equation   as a model for a fish population, where t is measured in weeks and c is a constant. For what values of c does the fish population always die out? as a model for a fish population, where t is measured in weeks and c is a constant. For what values of c does the fish population always die out?
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27
One model for the spread of a rumor is that the rate of spread is proportional to the product of the fraction of the population who have heard the rumor and the fraction who have not heard the rumor. Let's assume that the constant of proportionality is One model for the spread of a rumor is that the rate of spread is proportional to the product of the fraction of the population who have heard the rumor and the fraction who have not heard the rumor. Let's assume that the constant of proportionality is   . Write a differential equation that is satisfied by y. . Write a differential equation that is satisfied by y.
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28
The Pacific halibut fishery has been modeled by the differential equation The Pacific halibut fishery has been modeled by the differential equation   where   is the biomass (the total mass of the members of the population) in kilograms at time t (measured in years), the carrying capacity is estimated to be   and   per year. If   , find the biomass a year later. where The Pacific halibut fishery has been modeled by the differential equation   where   is the biomass (the total mass of the members of the population) in kilograms at time t (measured in years), the carrying capacity is estimated to be   and   per year. If   , find the biomass a year later. is the biomass (the total mass of the members of the population) in kilograms at time t (measured in years), the carrying capacity is estimated to be The Pacific halibut fishery has been modeled by the differential equation   where   is the biomass (the total mass of the members of the population) in kilograms at time t (measured in years), the carrying capacity is estimated to be   and   per year. If   , find the biomass a year later. and The Pacific halibut fishery has been modeled by the differential equation   where   is the biomass (the total mass of the members of the population) in kilograms at time t (measured in years), the carrying capacity is estimated to be   and   per year. If   , find the biomass a year later. per year. If The Pacific halibut fishery has been modeled by the differential equation   where   is the biomass (the total mass of the members of the population) in kilograms at time t (measured in years), the carrying capacity is estimated to be   and   per year. If   , find the biomass a year later. , find the biomass a year later.
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29
Suppose that a population grows according to a logistic model with carrying capacity Suppose that a population grows according to a logistic model with carrying capacity   and   per year. Write the logistic differential equation for these data. and Suppose that a population grows according to a logistic model with carrying capacity   and   per year. Write the logistic differential equation for these data. per year. Write the logistic differential equation for these data.
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30
Let c be a positive number. A differential equation of the form <strong>Let c be a positive number. A differential equation of the form   where k is a positive constant is called a doomsday equation because the exponent in the expression   is larger than the exponent 1 for natural growth. An especially prolific breed of rabbits has the growth term   . If   such rabbits breed initially and the warren has   rabbits after   months, then when is doomsday?</strong> A)   B)   C)   D)   E)   where k is a positive constant is called a doomsday equation because the exponent in the expression <strong>Let c be a positive number. A differential equation of the form   where k is a positive constant is called a doomsday equation because the exponent in the expression   is larger than the exponent 1 for natural growth. An especially prolific breed of rabbits has the growth term   . If   such rabbits breed initially and the warren has   rabbits after   months, then when is doomsday?</strong> A)   B)   C)   D)   E)   is larger than the exponent 1 for natural growth. An especially prolific breed of rabbits has the growth term <strong>Let c be a positive number. A differential equation of the form   where k is a positive constant is called a doomsday equation because the exponent in the expression   is larger than the exponent 1 for natural growth. An especially prolific breed of rabbits has the growth term   . If   such rabbits breed initially and the warren has   rabbits after   months, then when is doomsday?</strong> A)   B)   C)   D)   E)   . If <strong>Let c be a positive number. A differential equation of the form   where k is a positive constant is called a doomsday equation because the exponent in the expression   is larger than the exponent 1 for natural growth. An especially prolific breed of rabbits has the growth term   . If   such rabbits breed initially and the warren has   rabbits after   months, then when is doomsday?</strong> A)   B)   C)   D)   E)   such rabbits breed initially and the warren has <strong>Let c be a positive number. A differential equation of the form   where k is a positive constant is called a doomsday equation because the exponent in the expression   is larger than the exponent 1 for natural growth. An especially prolific breed of rabbits has the growth term   . If   such rabbits breed initially and the warren has   rabbits after   months, then when is doomsday?</strong> A)   B)   C)   D)   E)   rabbits after <strong>Let c be a positive number. A differential equation of the form   where k is a positive constant is called a doomsday equation because the exponent in the expression   is larger than the exponent 1 for natural growth. An especially prolific breed of rabbits has the growth term   . If   such rabbits breed initially and the warren has   rabbits after   months, then when is doomsday?</strong> A)   B)   C)   D)   E)   months, then when is doomsday?

A) <strong>Let c be a positive number. A differential equation of the form   where k is a positive constant is called a doomsday equation because the exponent in the expression   is larger than the exponent 1 for natural growth. An especially prolific breed of rabbits has the growth term   . If   such rabbits breed initially and the warren has   rabbits after   months, then when is doomsday?</strong> A)   B)   C)   D)   E)
B) <strong>Let c be a positive number. A differential equation of the form   where k is a positive constant is called a doomsday equation because the exponent in the expression   is larger than the exponent 1 for natural growth. An especially prolific breed of rabbits has the growth term   . If   such rabbits breed initially and the warren has   rabbits after   months, then when is doomsday?</strong> A)   B)   C)   D)   E)
C) <strong>Let c be a positive number. A differential equation of the form   where k is a positive constant is called a doomsday equation because the exponent in the expression   is larger than the exponent 1 for natural growth. An especially prolific breed of rabbits has the growth term   . If   such rabbits breed initially and the warren has   rabbits after   months, then when is doomsday?</strong> A)   B)   C)   D)   E)
D) <strong>Let c be a positive number. A differential equation of the form   where k is a positive constant is called a doomsday equation because the exponent in the expression   is larger than the exponent 1 for natural growth. An especially prolific breed of rabbits has the growth term   . If   such rabbits breed initially and the warren has   rabbits after   months, then when is doomsday?</strong> A)   B)   C)   D)   E)
E) <strong>Let c be a positive number. A differential equation of the form   where k is a positive constant is called a doomsday equation because the exponent in the expression   is larger than the exponent 1 for natural growth. An especially prolific breed of rabbits has the growth term   . If   such rabbits breed initially and the warren has   rabbits after   months, then when is doomsday?</strong> A)   B)   C)   D)   E)
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31
A curve passes through the point <strong>A curve passes through the point   and has the property that the slope of the curve at every point P is   times the y-coordinate P. What is the equation of the curve?</strong> A)   B)   C)   D)   E)   and has the property that the slope of the curve at every point P is <strong>A curve passes through the point   and has the property that the slope of the curve at every point P is   times the y-coordinate P. What is the equation of the curve?</strong> A)   B)   C)   D)   E)   times the y-coordinate P. What is the equation of the curve?

A) <strong>A curve passes through the point   and has the property that the slope of the curve at every point P is   times the y-coordinate P. What is the equation of the curve?</strong> A)   B)   C)   D)   E)
B) <strong>A curve passes through the point   and has the property that the slope of the curve at every point P is   times the y-coordinate P. What is the equation of the curve?</strong> A)   B)   C)   D)   E)
C) <strong>A curve passes through the point   and has the property that the slope of the curve at every point P is   times the y-coordinate P. What is the equation of the curve?</strong> A)   B)   C)   D)   E)
D) <strong>A curve passes through the point   and has the property that the slope of the curve at every point P is   times the y-coordinate P. What is the equation of the curve?</strong> A)   B)   C)   D)   E)
E) <strong>A curve passes through the point   and has the property that the slope of the curve at every point P is   times the y-coordinate P. What is the equation of the curve?</strong> A)   B)   C)   D)   E)
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Biologists stocked a lake with Biologists stocked a lake with   fish and estimated the carrying capacity (the maximal population for the fish of that species in that lake) to be   . The number of fish tripled in the first year. Assuming that the size of the fish population satisfies the logistic equation, find an expression for the size of the population after t years. fish and estimated the carrying capacity (the maximal population for the fish of that species in that lake) to be Biologists stocked a lake with   fish and estimated the carrying capacity (the maximal population for the fish of that species in that lake) to be   . The number of fish tripled in the first year. Assuming that the size of the fish population satisfies the logistic equation, find an expression for the size of the population after t years. . The number of fish tripled in the first year. Assuming that the size of the fish population satisfies the logistic equation, find an expression for the size of the population after t years.
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Solve the differential equation. <strong>Solve the differential equation.  </strong> A)   B)   C)   D)   E)

A) <strong>Solve the differential equation.  </strong> A)   B)   C)   D)   E)
B) <strong>Solve the differential equation.  </strong> A)   B)   C)   D)   E)
C) <strong>Solve the differential equation.  </strong> A)   B)   C)   D)   E)
D) <strong>Solve the differential equation.  </strong> A)   B)   C)   D)   E)
E) <strong>Solve the differential equation.  </strong> A)   B)   C)   D)   E)
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The population of the world was about 5.3 billion in 1990. Birth rates in the 1990s range from 35 to 40 million per year and death rates range from 15 to 20 million per year. Let's assume that the carrying capacity for world population is 100 billion. Use the logistic model to predict the world population in the 2,450 year. Calculate your answer in billions to one decimal place. (Because the initial population is small compared to the carrying capacity, you can take k to be an estimate of the initial relative growth rate.)

A)24.1 billion
B)32.9 billion
C)59.2 billion
D)78.3 billion
E)17.1 billion
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One model for the spread of an epidemic is that the rate of spread is jointly proportional to the number of infected people and the number of uninfected people. In an isolated town of <strong>One model for the spread of an epidemic is that the rate of spread is jointly proportional to the number of infected people and the number of uninfected people. In an isolated town of   inhabitants,   people have a disease at the beginning of the week and   have it at the end of the week. How long does it take for   of the population to be infected?</strong> A)   B)   C)   D)   E)   inhabitants, <strong>One model for the spread of an epidemic is that the rate of spread is jointly proportional to the number of infected people and the number of uninfected people. In an isolated town of   inhabitants,   people have a disease at the beginning of the week and   have it at the end of the week. How long does it take for   of the population to be infected?</strong> A)   B)   C)   D)   E)   people have a disease at the beginning of the week and <strong>One model for the spread of an epidemic is that the rate of spread is jointly proportional to the number of infected people and the number of uninfected people. In an isolated town of   inhabitants,   people have a disease at the beginning of the week and   have it at the end of the week. How long does it take for   of the population to be infected?</strong> A)   B)   C)   D)   E)   have it at the end of the week. How long does it take for <strong>One model for the spread of an epidemic is that the rate of spread is jointly proportional to the number of infected people and the number of uninfected people. In an isolated town of   inhabitants,   people have a disease at the beginning of the week and   have it at the end of the week. How long does it take for   of the population to be infected?</strong> A)   B)   C)   D)   E)   of the population to be infected?

A) <strong>One model for the spread of an epidemic is that the rate of spread is jointly proportional to the number of infected people and the number of uninfected people. In an isolated town of   inhabitants,   people have a disease at the beginning of the week and   have it at the end of the week. How long does it take for   of the population to be infected?</strong> A)   B)   C)   D)   E)
B) <strong>One model for the spread of an epidemic is that the rate of spread is jointly proportional to the number of infected people and the number of uninfected people. In an isolated town of   inhabitants,   people have a disease at the beginning of the week and   have it at the end of the week. How long does it take for   of the population to be infected?</strong> A)   B)   C)   D)   E)
C) <strong>One model for the spread of an epidemic is that the rate of spread is jointly proportional to the number of infected people and the number of uninfected people. In an isolated town of   inhabitants,   people have a disease at the beginning of the week and   have it at the end of the week. How long does it take for   of the population to be infected?</strong> A)   B)   C)   D)   E)
D) <strong>One model for the spread of an epidemic is that the rate of spread is jointly proportional to the number of infected people and the number of uninfected people. In an isolated town of   inhabitants,   people have a disease at the beginning of the week and   have it at the end of the week. How long does it take for   of the population to be infected?</strong> A)   B)   C)   D)   E)
E) <strong>One model for the spread of an epidemic is that the rate of spread is jointly proportional to the number of infected people and the number of uninfected people. In an isolated town of   inhabitants,   people have a disease at the beginning of the week and   have it at the end of the week. How long does it take for   of the population to be infected?</strong> A)   B)   C)   D)   E)
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A sum of <strong>A sum of   is invested at   interest. If   is the amount of the investment at time t for the case of continuous compounding, write a differential equation and an initial condition satisfied by   .</strong> A)   B)   C)   D)   E)   is invested at <strong>A sum of   is invested at   interest. If   is the amount of the investment at time t for the case of continuous compounding, write a differential equation and an initial condition satisfied by   .</strong> A)   B)   C)   D)   E)   interest. If <strong>A sum of   is invested at   interest. If   is the amount of the investment at time t for the case of continuous compounding, write a differential equation and an initial condition satisfied by   .</strong> A)   B)   C)   D)   E)   is the amount of the investment at time t for the case of continuous compounding, write a differential equation and an initial condition satisfied by <strong>A sum of   is invested at   interest. If   is the amount of the investment at time t for the case of continuous compounding, write a differential equation and an initial condition satisfied by   .</strong> A)   B)   C)   D)   E)   .

A) <strong>A sum of   is invested at   interest. If   is the amount of the investment at time t for the case of continuous compounding, write a differential equation and an initial condition satisfied by   .</strong> A)   B)   C)   D)   E)
B) <strong>A sum of   is invested at   interest. If   is the amount of the investment at time t for the case of continuous compounding, write a differential equation and an initial condition satisfied by   .</strong> A)   B)   C)   D)   E)
C) <strong>A sum of   is invested at   interest. If   is the amount of the investment at time t for the case of continuous compounding, write a differential equation and an initial condition satisfied by   .</strong> A)   B)   C)   D)   E)
D) <strong>A sum of   is invested at   interest. If   is the amount of the investment at time t for the case of continuous compounding, write a differential equation and an initial condition satisfied by   .</strong> A)   B)   C)   D)   E)
E) <strong>A sum of   is invested at   interest. If   is the amount of the investment at time t for the case of continuous compounding, write a differential equation and an initial condition satisfied by   .</strong> A)   B)   C)   D)   E)
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Suppose that a population develops according to the logistic equation <strong>Suppose that a population develops according to the logistic equation   , where t is measured in weeks. What is the carrying capacity?</strong> A)   B)   C)   D)   E)   , where t is measured in weeks. What is the carrying capacity?

A) <strong>Suppose that a population develops according to the logistic equation   , where t is measured in weeks. What is the carrying capacity?</strong> A)   B)   C)   D)   E)
B) <strong>Suppose that a population develops according to the logistic equation   , where t is measured in weeks. What is the carrying capacity?</strong> A)   B)   C)   D)   E)
C) <strong>Suppose that a population develops according to the logistic equation   , where t is measured in weeks. What is the carrying capacity?</strong> A)   B)   C)   D)   E)
D) <strong>Suppose that a population develops according to the logistic equation   , where t is measured in weeks. What is the carrying capacity?</strong> A)   B)   C)   D)   E)
E) <strong>Suppose that a population develops according to the logistic equation   , where t is measured in weeks. What is the carrying capacity?</strong> A)   B)   C)   D)   E)
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One model for the spread of an epidemic is that the rate of spread is jointly proportional to the number of infected people and the number of uninfected people. In an isolated town of One model for the spread of an epidemic is that the rate of spread is jointly proportional to the number of infected people and the number of uninfected people. In an isolated town of   inhabitants,   people have a disease at the beginning of the week and   have it at the end of the week. How long does it take for   of the population to be infected? inhabitants, One model for the spread of an epidemic is that the rate of spread is jointly proportional to the number of infected people and the number of uninfected people. In an isolated town of   inhabitants,   people have a disease at the beginning of the week and   have it at the end of the week. How long does it take for   of the population to be infected? people have a disease at the beginning of the week and One model for the spread of an epidemic is that the rate of spread is jointly proportional to the number of infected people and the number of uninfected people. In an isolated town of   inhabitants,   people have a disease at the beginning of the week and   have it at the end of the week. How long does it take for   of the population to be infected? have it at the end of the week. How long does it take for One model for the spread of an epidemic is that the rate of spread is jointly proportional to the number of infected people and the number of uninfected people. In an isolated town of   inhabitants,   people have a disease at the beginning of the week and   have it at the end of the week. How long does it take for   of the population to be infected? of the population to be infected?
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A common inhabitant of human intestines is the bacterium Escherichia coli. A cell of this bacterium in a nutrient-broth medium divides into two cells every <strong>A common inhabitant of human intestines is the bacterium Escherichia coli. A cell of this bacterium in a nutrient-broth medium divides into two cells every   . The initial population of a culture is   cells. Find the number of cells after   hours.</strong> A)   B)   C)   D)   E)   . The initial population of a culture is <strong>A common inhabitant of human intestines is the bacterium Escherichia coli. A cell of this bacterium in a nutrient-broth medium divides into two cells every   . The initial population of a culture is   cells. Find the number of cells after   hours.</strong> A)   B)   C)   D)   E)   cells. Find the number of cells after <strong>A common inhabitant of human intestines is the bacterium Escherichia coli. A cell of this bacterium in a nutrient-broth medium divides into two cells every   . The initial population of a culture is   cells. Find the number of cells after   hours.</strong> A)   B)   C)   D)   E)   hours.

A) <strong>A common inhabitant of human intestines is the bacterium Escherichia coli. A cell of this bacterium in a nutrient-broth medium divides into two cells every   . The initial population of a culture is   cells. Find the number of cells after   hours.</strong> A)   B)   C)   D)   E)
B) <strong>A common inhabitant of human intestines is the bacterium Escherichia coli. A cell of this bacterium in a nutrient-broth medium divides into two cells every   . The initial population of a culture is   cells. Find the number of cells after   hours.</strong> A)   B)   C)   D)   E)
C) <strong>A common inhabitant of human intestines is the bacterium Escherichia coli. A cell of this bacterium in a nutrient-broth medium divides into two cells every   . The initial population of a culture is   cells. Find the number of cells after   hours.</strong> A)   B)   C)   D)   E)
D) <strong>A common inhabitant of human intestines is the bacterium Escherichia coli. A cell of this bacterium in a nutrient-broth medium divides into two cells every   . The initial population of a culture is   cells. Find the number of cells after   hours.</strong> A)   B)   C)   D)   E)
E) <strong>A common inhabitant of human intestines is the bacterium Escherichia coli. A cell of this bacterium in a nutrient-broth medium divides into two cells every   . The initial population of a culture is   cells. Find the number of cells after   hours.</strong> A)   B)   C)   D)   E)
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Solve the differential equation. <strong>Solve the differential equation.  </strong> A)   B)   C)   D)   E)

A) <strong>Solve the differential equation.  </strong> A)   B)   C)   D)   E)
B) <strong>Solve the differential equation.  </strong> A)   B)   C)   D)   E)
C) <strong>Solve the differential equation.  </strong> A)   B)   C)   D)   E)
D) <strong>Solve the differential equation.  </strong> A)   B)   C)   D)   E)
E) <strong>Solve the differential equation.  </strong> A)   B)   C)   D)   E)
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Experiments show that if the chemical reaction Experiments show that if the chemical reaction   takes place at   , the rate of reaction of dinitrogen pentoxide is proportional to its concentration as follows :   How long will the reaction take to reduce the concentration of   to 50% of its original value? takes place at Experiments show that if the chemical reaction   takes place at   , the rate of reaction of dinitrogen pentoxide is proportional to its concentration as follows :   How long will the reaction take to reduce the concentration of   to 50% of its original value? , the rate of reaction of dinitrogen pentoxide is proportional to its concentration as follows : Experiments show that if the chemical reaction   takes place at   , the rate of reaction of dinitrogen pentoxide is proportional to its concentration as follows :   How long will the reaction take to reduce the concentration of   to 50% of its original value? How long will the reaction take to reduce the concentration of Experiments show that if the chemical reaction   takes place at   , the rate of reaction of dinitrogen pentoxide is proportional to its concentration as follows :   How long will the reaction take to reduce the concentration of   to 50% of its original value? to 50% of its original value?
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42
Solve the differential equation. Solve the differential equation.
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A certain small country has $20 billion in paper currency in circulation, and each day $70 million comes into the country's banks. The government decides to introduce new currency by having the banks replace old bills with new ones whenever old currency comes into the banks. Let A certain small country has $20 billion in paper currency in circulation, and each day $70 million comes into the country's banks. The government decides to introduce new currency by having the banks replace old bills with new ones whenever old currency comes into the banks. Let   denote the amount of new currency in circulation at time t with   . Formulate and solve a mathematical model in the form of an initial-value problem that represents the flow of the new currency into circulation (in billions per day). denote the amount of new currency in circulation at time t with A certain small country has $20 billion in paper currency in circulation, and each day $70 million comes into the country's banks. The government decides to introduce new currency by having the banks replace old bills with new ones whenever old currency comes into the banks. Let   denote the amount of new currency in circulation at time t with   . Formulate and solve a mathematical model in the form of an initial-value problem that represents the flow of the new currency into circulation (in billions per day). . Formulate and solve a mathematical model in the form of an initial-value problem that represents the "flow" of the new currency into circulation (in billions per day).
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44
Solve the differential equation. Solve the differential equation.
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Find the solution of the differential equation that satisfies the initial condition Find the solution of the differential equation that satisfies the initial condition   .  . Find the solution of the differential equation that satisfies the initial condition   .
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Find the orthogonal trajectories of the family of curves. <strong>Find the orthogonal trajectories of the family of curves.  </strong> A)   B)   C)   D)   E)

A) <strong>Find the orthogonal trajectories of the family of curves.  </strong> A)   B)   C)   D)   E)
B) <strong>Find the orthogonal trajectories of the family of curves.  </strong> A)   B)   C)   D)   E)
C) <strong>Find the orthogonal trajectories of the family of curves.  </strong> A)   B)   C)   D)   E)
D) <strong>Find the orthogonal trajectories of the family of curves.  </strong> A)   B)   C)   D)   E)
E) <strong>Find the orthogonal trajectories of the family of curves.  </strong> A)   B)   C)   D)   E)
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47
Select a direction field for the differential equation Select a direction field for the differential equation   from a set of direction fields labeled I-IV.  from a set of direction fields labeled I-IV. Select a direction field for the differential equation   from a set of direction fields labeled I-IV.
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A population is modeled by the differential equation. <strong>A population is modeled by the differential equation.   For what values of P is the population increasing?</strong> A)   B)   C)   D)   E)   For what values of P is the population increasing?

A) <strong>A population is modeled by the differential equation.   For what values of P is the population increasing?</strong> A)   B)   C)   D)   E)
B) <strong>A population is modeled by the differential equation.   For what values of P is the population increasing?</strong> A)   B)   C)   D)   E)
C) <strong>A population is modeled by the differential equation.   For what values of P is the population increasing?</strong> A)   B)   C)   D)   E)
D) <strong>A population is modeled by the differential equation.   For what values of P is the population increasing?</strong> A)   B)   C)   D)   E)
E) <strong>A population is modeled by the differential equation.   For what values of P is the population increasing?</strong> A)   B)   C)   D)   E)
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Choose the differential equation corresponding to this direction field. <strong>Choose the differential equation corresponding to this direction field.  </strong> A)   B)   C)   D)   E)

A) <strong>Choose the differential equation corresponding to this direction field.  </strong> A)   B)   C)   D)   E)
B) <strong>Choose the differential equation corresponding to this direction field.  </strong> A)   B)   C)   D)   E)
C) <strong>Choose the differential equation corresponding to this direction field.  </strong> A)   B)   C)   D)   E)
D) <strong>Choose the differential equation corresponding to this direction field.  </strong> A)   B)   C)   D)   E)
E) <strong>Choose the differential equation corresponding to this direction field.  </strong> A)   B)   C)   D)   E)
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50
Find the orthogonal trajectories of the family of curves. Find the orthogonal trajectories of the family of curves.
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51
Solve the differential equation. Solve the differential equation.
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A tank contains A tank contains   L of brine with   kg of dissolved salt. Pure water enters the tank at a rate of   L/min. The solution is kept thoroughly mixed and drains from the tank at the same rate. How much salt is in the tank after   minutes? L of brine with A tank contains   L of brine with   kg of dissolved salt. Pure water enters the tank at a rate of   L/min. The solution is kept thoroughly mixed and drains from the tank at the same rate. How much salt is in the tank after   minutes? kg of dissolved salt. Pure water enters the tank at a rate of A tank contains   L of brine with   kg of dissolved salt. Pure water enters the tank at a rate of   L/min. The solution is kept thoroughly mixed and drains from the tank at the same rate. How much salt is in the tank after   minutes? L/min. The solution is kept thoroughly mixed and drains from the tank at the same rate. How much salt is in the tank after A tank contains   L of brine with   kg of dissolved salt. Pure water enters the tank at a rate of   L/min. The solution is kept thoroughly mixed and drains from the tank at the same rate. How much salt is in the tank after   minutes? minutes?
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Which equation does the function <strong>Which equation does the function   satisfy?</strong> A)   B)   C)   D)   E)   satisfy?

A) <strong>Which equation does the function   satisfy?</strong> A)   B)   C)   D)   E)
B) <strong>Which equation does the function   satisfy?</strong> A)   B)   C)   D)   E)
C) <strong>Which equation does the function   satisfy?</strong> A)   B)   C)   D)   E)
D) <strong>Which equation does the function   satisfy?</strong> A)   B)   C)   D)   E)
E) <strong>Which equation does the function   satisfy?</strong> A)   B)   C)   D)   E)
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Solve the initial-value problem. <strong>Solve the initial-value problem.  </strong> A)   B)   C)   D)   E)

A) <strong>Solve the initial-value problem.  </strong> A)   B)   C)   D)   E)
B) <strong>Solve the initial-value problem.  </strong> A)   B)   C)   D)   E)
C) <strong>Solve the initial-value problem.  </strong> A)   B)   C)   D)   E)
D) <strong>Solve the initial-value problem.  </strong> A)   B)   C)   D)   E)
E) <strong>Solve the initial-value problem.  </strong> A)   B)   C)   D)   E)
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Find the solution of the differential equation Find the solution of the differential equation   that satisfies the initial condition   . that satisfies the initial condition Find the solution of the differential equation   that satisfies the initial condition   . .
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Use Euler's method with step size 0.1 to estimate Use Euler's method with step size 0.1 to estimate   , where   is the solution of the initial-value problem. Round your answer to four decimal places.  , where Use Euler's method with step size 0.1 to estimate   , where   is the solution of the initial-value problem. Round your answer to four decimal places.  is the solution of the initial-value problem. Round your answer to four decimal places. Use Euler's method with step size 0.1 to estimate   , where   is the solution of the initial-value problem. Round your answer to four decimal places.
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Use Euler's method with step size 0.25 to estimate <strong>Use Euler's method with step size 0.25 to estimate   , where   is the solution of the initial-value problem. Round your answer to four decimal places.  </strong> A)   B)   C)   D)   E)   , where <strong>Use Euler's method with step size 0.25 to estimate   , where   is the solution of the initial-value problem. Round your answer to four decimal places.  </strong> A)   B)   C)   D)   E)   is the solution of the initial-value problem. Round your answer to four decimal places. <strong>Use Euler's method with step size 0.25 to estimate   , where   is the solution of the initial-value problem. Round your answer to four decimal places.  </strong> A)   B)   C)   D)   E)

A) <strong>Use Euler's method with step size 0.25 to estimate   , where   is the solution of the initial-value problem. Round your answer to four decimal places.  </strong> A)   B)   C)   D)   E)
B) <strong>Use Euler's method with step size 0.25 to estimate   , where   is the solution of the initial-value problem. Round your answer to four decimal places.  </strong> A)   B)   C)   D)   E)
C) <strong>Use Euler's method with step size 0.25 to estimate   , where   is the solution of the initial-value problem. Round your answer to four decimal places.  </strong> A)   B)   C)   D)   E)
D) <strong>Use Euler's method with step size 0.25 to estimate   , where   is the solution of the initial-value problem. Round your answer to four decimal places.  </strong> A)   B)   C)   D)   E)
E) <strong>Use Euler's method with step size 0.25 to estimate   , where   is the solution of the initial-value problem. Round your answer to four decimal places.  </strong> A)   B)   C)   D)   E)
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Solve the differential equation. <strong>Solve the differential equation.  </strong> A)   B)   C)   D)   E)

A) <strong>Solve the differential equation.  </strong> A)   B)   C)   D)   E)
B) <strong>Solve the differential equation.  </strong> A)   B)   C)   D)   E)
C) <strong>Solve the differential equation.  </strong> A)   B)   C)   D)   E)
D) <strong>Solve the differential equation.  </strong> A)   B)   C)   D)   E)
E) <strong>Solve the differential equation.  </strong> A)   B)   C)   D)   E)
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The solution of the differential equation The solution of the differential equation   satisfies the initial condition   . Find the limit.  satisfies the initial condition The solution of the differential equation   satisfies the initial condition   . Find the limit.  .
Find the limit. The solution of the differential equation   satisfies the initial condition   . Find the limit.
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Kirchhoff's Law gives us the derivative equation Kirchhoff's Law gives us the derivative equation   . If   , use Euler's method with step size 0.1 to estimate   after 0.3 second. .
If Kirchhoff's Law gives us the derivative equation   . If   , use Euler's method with step size 0.1 to estimate   after 0.3 second. , use Euler's method with step size 0.1 to estimate Kirchhoff's Law gives us the derivative equation   . If   , use Euler's method with step size 0.1 to estimate   after 0.3 second. after 0.3 second.
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For what nonzero values of k does the function <strong>For what nonzero values of k does the function   satisfy the differential equation   for all values of A and B? </strong> A)   B)   C)   D)   E)   satisfy the differential equation <strong>For what nonzero values of k does the function   satisfy the differential equation   for all values of A and B? </strong> A)   B)   C)   D)   E)   for all values of A and B?

A) <strong>For what nonzero values of k does the function   satisfy the differential equation   for all values of A and B? </strong> A)   B)   C)   D)   E)
B) <strong>For what nonzero values of k does the function   satisfy the differential equation   for all values of A and B? </strong> A)   B)   C)   D)   E)
C) <strong>For what nonzero values of k does the function   satisfy the differential equation   for all values of A and B? </strong> A)   B)   C)   D)   E)
D) <strong>For what nonzero values of k does the function   satisfy the differential equation   for all values of A and B? </strong> A)   B)   C)   D)   E)
E) <strong>For what nonzero values of k does the function   satisfy the differential equation   for all values of A and B? </strong> A)   B)   C)   D)   E)
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For what values of k does the function <strong>For what values of k does the function   satisfy the differential equation   ? </strong> A)   B)   C)   D)   E)   satisfy the differential equation <strong>For what values of k does the function   satisfy the differential equation   ? </strong> A)   B)   C)   D)   E)   ?

A) <strong>For what values of k does the function   satisfy the differential equation   ? </strong> A)   B)   C)   D)   E)
B) <strong>For what values of k does the function   satisfy the differential equation   ? </strong> A)   B)   C)   D)   E)
C) <strong>For what values of k does the function   satisfy the differential equation   ? </strong> A)   B)   C)   D)   E)
D) <strong>For what values of k does the function   satisfy the differential equation   ? </strong> A)   B)   C)   D)   E)
E) <strong>For what values of k does the function   satisfy the differential equation   ? </strong> A)   B)   C)   D)   E)
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Newton's Law of Cooling states that the rate of cooling of an object is proportional to the temperature difference between the object and its surroundings. Suppose that a roast turkey is taken from an oven when its temperature has reached <strong>Newton's Law of Cooling states that the rate of cooling of an object is proportional to the temperature difference between the object and its surroundings. Suppose that a roast turkey is taken from an oven when its temperature has reached   and is placed on a table in a room where the temperature is   . If   is the temperature of the turkey after t minutes, then Newton's Law of Cooling implies that   . This could be solved as a separable differential equation. Another method is to make the change of variable   . If the temperature of the turkey is   after half an hour, what is the temperature after 35 min?</strong> A)   B)   C)   D)   E)   and is placed on a table in a room where the temperature is <strong>Newton's Law of Cooling states that the rate of cooling of an object is proportional to the temperature difference between the object and its surroundings. Suppose that a roast turkey is taken from an oven when its temperature has reached   and is placed on a table in a room where the temperature is   . If   is the temperature of the turkey after t minutes, then Newton's Law of Cooling implies that   . This could be solved as a separable differential equation. Another method is to make the change of variable   . If the temperature of the turkey is   after half an hour, what is the temperature after 35 min?</strong> A)   B)   C)   D)   E)   . If <strong>Newton's Law of Cooling states that the rate of cooling of an object is proportional to the temperature difference between the object and its surroundings. Suppose that a roast turkey is taken from an oven when its temperature has reached   and is placed on a table in a room where the temperature is   . If   is the temperature of the turkey after t minutes, then Newton's Law of Cooling implies that   . This could be solved as a separable differential equation. Another method is to make the change of variable   . If the temperature of the turkey is   after half an hour, what is the temperature after 35 min?</strong> A)   B)   C)   D)   E)   is the temperature of the turkey after t minutes, then Newton's Law of Cooling implies that <strong>Newton's Law of Cooling states that the rate of cooling of an object is proportional to the temperature difference between the object and its surroundings. Suppose that a roast turkey is taken from an oven when its temperature has reached   and is placed on a table in a room where the temperature is   . If   is the temperature of the turkey after t minutes, then Newton's Law of Cooling implies that   . This could be solved as a separable differential equation. Another method is to make the change of variable   . If the temperature of the turkey is   after half an hour, what is the temperature after 35 min?</strong> A)   B)   C)   D)   E)   . This could be solved as a separable differential equation. Another method is to make the change of variable <strong>Newton's Law of Cooling states that the rate of cooling of an object is proportional to the temperature difference between the object and its surroundings. Suppose that a roast turkey is taken from an oven when its temperature has reached   and is placed on a table in a room where the temperature is   . If   is the temperature of the turkey after t minutes, then Newton's Law of Cooling implies that   . This could be solved as a separable differential equation. Another method is to make the change of variable   . If the temperature of the turkey is   after half an hour, what is the temperature after 35 min?</strong> A)   B)   C)   D)   E)   . If the temperature of the turkey is <strong>Newton's Law of Cooling states that the rate of cooling of an object is proportional to the temperature difference between the object and its surroundings. Suppose that a roast turkey is taken from an oven when its temperature has reached   and is placed on a table in a room where the temperature is   . If   is the temperature of the turkey after t minutes, then Newton's Law of Cooling implies that   . This could be solved as a separable differential equation. Another method is to make the change of variable   . If the temperature of the turkey is   after half an hour, what is the temperature after 35 min?</strong> A)   B)   C)   D)   E)   after half an hour, what is the temperature after 35 min?

A) <strong>Newton's Law of Cooling states that the rate of cooling of an object is proportional to the temperature difference between the object and its surroundings. Suppose that a roast turkey is taken from an oven when its temperature has reached   and is placed on a table in a room where the temperature is   . If   is the temperature of the turkey after t minutes, then Newton's Law of Cooling implies that   . This could be solved as a separable differential equation. Another method is to make the change of variable   . If the temperature of the turkey is   after half an hour, what is the temperature after 35 min?</strong> A)   B)   C)   D)   E)
B) <strong>Newton's Law of Cooling states that the rate of cooling of an object is proportional to the temperature difference between the object and its surroundings. Suppose that a roast turkey is taken from an oven when its temperature has reached   and is placed on a table in a room where the temperature is   . If   is the temperature of the turkey after t minutes, then Newton's Law of Cooling implies that   . This could be solved as a separable differential equation. Another method is to make the change of variable   . If the temperature of the turkey is   after half an hour, what is the temperature after 35 min?</strong> A)   B)   C)   D)   E)
C) <strong>Newton's Law of Cooling states that the rate of cooling of an object is proportional to the temperature difference between the object and its surroundings. Suppose that a roast turkey is taken from an oven when its temperature has reached   and is placed on a table in a room where the temperature is   . If   is the temperature of the turkey after t minutes, then Newton's Law of Cooling implies that   . This could be solved as a separable differential equation. Another method is to make the change of variable   . If the temperature of the turkey is   after half an hour, what is the temperature after 35 min?</strong> A)   B)   C)   D)   E)
D) <strong>Newton's Law of Cooling states that the rate of cooling of an object is proportional to the temperature difference between the object and its surroundings. Suppose that a roast turkey is taken from an oven when its temperature has reached   and is placed on a table in a room where the temperature is   . If   is the temperature of the turkey after t minutes, then Newton's Law of Cooling implies that   . This could be solved as a separable differential equation. Another method is to make the change of variable   . If the temperature of the turkey is   after half an hour, what is the temperature after 35 min?</strong> A)   B)   C)   D)   E)
E) <strong>Newton's Law of Cooling states that the rate of cooling of an object is proportional to the temperature difference between the object and its surroundings. Suppose that a roast turkey is taken from an oven when its temperature has reached   and is placed on a table in a room where the temperature is   . If   is the temperature of the turkey after t minutes, then Newton's Law of Cooling implies that   . This could be solved as a separable differential equation. Another method is to make the change of variable   . If the temperature of the turkey is   after half an hour, what is the temperature after 35 min?</strong> A)   B)   C)   D)   E)
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A population is modeled by the differential equation A population is modeled by the differential equation   . For what values of P is the population decreasing? .
For what values of P is the population decreasing?
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Which of the following functions are the constant solutions of the equation Which of the following functions are the constant solutions of the equation   a.   b.   c.   d.   e.
a. Which of the following functions are the constant solutions of the equation   a.   b.   c.   d.   e.
b. Which of the following functions are the constant solutions of the equation   a.   b.   c.   d.   e.
c. Which of the following functions are the constant solutions of the equation   a.   b.   c.   d.   e.
d. Which of the following functions are the constant solutions of the equation   a.   b.   c.   d.   e.
e. Which of the following functions are the constant solutions of the equation   a.   b.   c.   d.   e.
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A sum of A sum of   is invested at   interest. If   is the amount of the investment at time t for the case of continuous compounding, write a differential equation and an initial condition satisfied by   . is invested at A sum of   is invested at   interest. If   is the amount of the investment at time t for the case of continuous compounding, write a differential equation and an initial condition satisfied by   . interest. If A sum of   is invested at   interest. If   is the amount of the investment at time t for the case of continuous compounding, write a differential equation and an initial condition satisfied by   . is the amount of the investment at time t for the case of continuous compounding, write a differential equation and an initial condition satisfied by A sum of   is invested at   interest. If   is the amount of the investment at time t for the case of continuous compounding, write a differential equation and an initial condition satisfied by   . .
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A function A function   satisfies the differential equation   . What are the constant solutions of the equation? satisfies the differential equation A function   satisfies the differential equation   . What are the constant solutions of the equation? .
What are the constant solutions of the equation?
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