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Deck 9: Differential Equations
ملء الشاشة (f)
سؤال
Solve the initial-value problem. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Solve the differential equation. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Solve the initial-value problem. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Determine whether the differential equation is linear. 
A)the equation is not linear
B)the equation is linear
A)the equation is not linear
B)the equation is linear
سؤال
Solve the differential equation. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
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. 
A) 0.75 A
B)
C)
D)
E)
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. A) 0.75 A
B)
C)
D)
E)
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 
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 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.
سؤال
Solve the initial-value problem. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
We modeled populations of aphids and ladybugs with a Lotka-Volterra system. Suppose we modify those equations as follows: 
, 
A)
B)
C)
D)
E)
, A)
B)
C)
D)
E)
سؤال
A phase trajectory is shown for populations of rabbits 
and foxes 
. Describe how each population changes as time goes by. 
Select the correct statement.
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 . Describe how each population changes as time goes by. Select the correct statement.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. سؤال
Which of the following functions is a solution of the differential equation? 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Solve the differential equation. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Solve the differential equation. 
سؤال
Determine whether the differential equation is linear. 
سؤال
Solve the initial-value problem. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Solve the initial-value problem. 
سؤال
Solve the initial-value problem. 
سؤال
Find the solution of the initial-value problem and use it to find the population when 
. 
. سؤال
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.
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 as a reasonable model for learning, where r is a positive constant. Solve it as a linear differential equation.A)
B)
C)
D)
E)
سؤال
Solve the initial-value problem. 
سؤال
Suppose that a population grows according to a logistic model with carrying capacity 
and 
per year. Choose the logistic differential equation for these data.
A)
B)
C)
D)
E)
and per year. Choose the logistic differential equation for these data.A)
B)
C)
D)
E)
سؤال
Let 
.
What are the equilibrium solutions?
.What are the equilibrium solutions?
سؤال
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 pressure is 
at sea level and 
at 
. What is the pressure at an altitude of 
?
the pressure is at sea level and at . What is the pressure at an altitude of ? سؤال
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 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? سؤال
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? 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 
. Write a differential equation that is satisfied by y.
. Write a differential equation that is satisfied by y. سؤال
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 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. سؤال
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 per year. Write the logistic differential equation for these data. سؤال
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?
A)
B)
C)
D)
E)
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?A)
B)
C)
D)
E)
سؤال
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?
A)
B)
C)
D)
E)
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?A)
B)
C)
D)
E)
سؤال
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 . 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. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
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 
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?
A)
B)
C)
D)
E)
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?A)
B)
C)
D)
E)
سؤال
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 
.
A)
B)
C)
D)
E)
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 .A)
B)
C)
D)
E)
سؤال
Suppose that a population develops according to the logistic equation 
, where t is measured in weeks. What is the carrying capacity?
A)
B)
C)
D)
E)
, where t is measured in weeks. What is the carrying capacity?A)
B)
C)
D)
E)
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 
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, 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? 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 
. The initial population of a culture is 
cells. Find the number of cells after 
hours.
A)
B)
C)
D)
E)
. The initial population of a culture is cells. Find the number of cells after hours.A)
B)
C)
D)
E)
سؤال
Solve the differential equation. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
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 , 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? سؤال
Solve the differential equation. 
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 
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 . 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. 
سؤال
Find the solution of the differential equation that satisfies the initial condition 
. 
. سؤال
Find the orthogonal trajectories of the family of curves. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
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. سؤال
A population is modeled by the differential equation. 
For what values of P is the population increasing?
A)
B)
C)
D)
E)
For what values of P is the population increasing?A)
B)
C)
D)
E)
سؤال
Choose the differential equation corresponding to this direction field. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Find the orthogonal trajectories of the family of curves. 
سؤال
Solve the differential equation. 
سؤال
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 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? سؤال
Which equation does the function 
satisfy?
A)
B)
C)
D)
E)
satisfy?A)
B)
C)
D)
E)
سؤال
Solve the initial-value problem. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Find the solution of the differential equation 
that satisfies the initial condition 
.
that satisfies the initial condition . سؤال
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 is the solution of the initial-value problem. Round your answer to four decimal places. سؤال
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. 
A)
B)
C)
D)
E)
, where is the solution of the initial-value problem. Round your answer to four decimal places. A)
B)
C)
D)
E)
سؤال
Solve the differential equation. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
The solution of the differential equation 
satisfies the initial condition 
.
Find the limit.
satisfies the initial condition .Find the limit.
سؤال
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
, use Euler's method with step size 0.1 to estimate after 0.3 second. سؤال
For what nonzero values of k does the function 
satisfy the differential equation 
for all values of A and B?
A)
B)
C)
D)
E)
satisfy the differential equation for all values of A and B? A)
B)
C)
D)
E)
سؤال
For what values of k does the function 
satisfy the differential equation 
?
A)
B)
C)
D)
E)
satisfy the differential equation ? A)
B)
C)
D)
E)
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 
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?
A)
B)
C)
D)
E)
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?A)
B)
C)
D)
E)
سؤال
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?
سؤال
Which of the following functions are the constant solutions of the equation 
a.
b.
c.
d.
e.
a.
b.
c.
d.
e.
سؤال
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 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 . سؤال
A function 
satisfies the differential equation 
.
What are the constant solutions of the equation?
satisfies the differential equation .What are the constant solutions of the equation?
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ملء الشاشة (f)
Deck 9: Differential Equations
1
Solve the initial-value problem.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
2
Solve the differential equation.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
3
Solve the initial-value problem.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
4
Determine whether the differential equation is linear.
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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5
Solve the differential equation.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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6
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.
A) 0.75 A
B)
C)
D)
E)
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. 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 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 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.
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8
Solve the initial-value problem.
A)
B)
C)
D)
E)
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: ,
A)
B)
C)
D)
E)
, A)
B)
C)
D)
E)
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10
A phase trajectory is shown for populations of rabbits and foxes . Describe how each population changes as time goes by. Select the correct statement.
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 . Describe how each population changes as time goes by. Select the correct statement.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. فتح الحزمة
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11
Which of the following functions is a solution of the differential equation?
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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12
Solve the differential equation.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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13
Solve the differential equation.
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14
Determine whether the differential equation is linear.
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15
Solve the initial-value problem.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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16
Solve the initial-value problem.
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17
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 .
. فتح الحزمة
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19
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.
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 as a reasonable model for learning, where r is a positive constant. Solve it as a linear differential equation.A)
B)
C)
D)
E)
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20
Solve the initial-value problem.
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21
Suppose that a population grows according to a logistic model with carrying capacity and per year. Choose the logistic differential equation for these data.
A)
B)
C)
D)
E)
and per year. Choose the logistic differential equation for these data.A)
B)
C)
D)
E)
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22
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
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 pressure is at sea level and at . What is the pressure at an altitude of ?
the pressure is at sea level and at . What is the pressure at an altitude of ? فتح الحزمة
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25
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 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? فتح الحزمة
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26
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? فتح الحزمة
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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 . Write a differential equation that is satisfied by y.
. Write a differential equation that is satisfied by y. فتح الحزمة
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28
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 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. فتح الحزمة
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29
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 per year. Write the logistic differential equation for these data. فتح الحزمة
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30
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?
A)
B)
C)
D)
E)
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?A)
B)
C)
D)
E)
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31
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?
A)
B)
C)
D)
E)
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?A)
B)
C)
D)
E)
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32
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 . 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. فتح الحزمة
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33
Solve the differential equation.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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34
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
A)24.1 billion
B)32.9 billion
C)59.2 billion
D)78.3 billion
E)17.1 billion
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35
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?
A)
B)
C)
D)
E)
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?A)
B)
C)
D)
E)
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36
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 .
A)
B)
C)
D)
E)
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 .A)
B)
C)
D)
E)
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37
Suppose that a population develops according to the logistic equation , where t is measured in weeks. What is the carrying capacity?
A)
B)
C)
D)
E)
, where t is measured in weeks. What is the carrying capacity?A)
B)
C)
D)
E)
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38
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, 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? فتح الحزمة
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39
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.
A)
B)
C)
D)
E)
. The initial population of a culture is cells. Find the number of cells after hours.A)
B)
C)
D)
E)
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40
Solve the differential equation.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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41
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 , 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? فتح الحزمة
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42
Solve the differential equation.
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43
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 . 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). فتح الحزمة
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44
Solve the differential equation.
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45
Find the solution of the differential equation that satisfies the initial condition .
. فتح الحزمة
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46
Find the orthogonal trajectories of the family of curves.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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47
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. فتح الحزمة
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48
A population is modeled by the differential equation. For what values of P is the population increasing?
A)
B)
C)
D)
E)
For what values of P is the population increasing?A)
B)
C)
D)
E)
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49
Choose the differential equation corresponding to this direction field.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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50
Find the orthogonal trajectories of the family of curves.
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51
Solve the differential equation.
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52
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 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? فتح الحزمة
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53
Which equation does the function satisfy?
A)
B)
C)
D)
E)
satisfy?A)
B)
C)
D)
E)
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54
Solve the initial-value problem.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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55
Find the solution of the differential equation that satisfies the initial condition .
that satisfies the initial condition . فتح الحزمة
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56
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 is the solution of the initial-value problem. Round your answer to four decimal places. فتح الحزمة
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57
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.
A)
B)
C)
D)
E)
, where is the solution of the initial-value problem. Round your answer to four decimal places. A)
B)
C)
D)
E)
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58
Solve the differential equation.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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59
The solution of the differential equation satisfies the initial condition .
Find the limit.
satisfies the initial condition .Find the limit.
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60
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
, use Euler's method with step size 0.1 to estimate after 0.3 second. فتح الحزمة
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61
For what nonzero values of k does the function satisfy the differential equation for all values of A and B?
A)
B)
C)
D)
E)
satisfy the differential equation for all values of A and B? A)
B)
C)
D)
E)
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62
For what values of k does the function satisfy the differential equation ?
A)
B)
C)
D)
E)
satisfy the differential equation ? A)
B)
C)
D)
E)
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63
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?
A)
B)
C)
D)
E)
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?A)
B)
C)
D)
E)
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64
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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65
Which of the following functions are the constant solutions of the equation
a.
b.
c.
d.
e.
a.
b.
c.
d.
e.
فتح الحزمة
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66
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 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 . فتح الحزمة
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67
A function satisfies the differential equation .
What are the constant solutions of the equation?
satisfies the differential equation .What are the constant solutions of the equation?
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