Question 1

A population is modeled by the differential equation  For what values of  is the population decreasing?

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Question 2

Determine whether the differential equation is linear.

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Question 3

Solve the differential equation.

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Question 4

Find the solution of the initial-value problem and use it to find the population when

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The answer of Find the solution of the initial-value problem...

Question 5

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

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Question 6

Find the solution of the differential equation  hat satisfies the initial condition

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Question 7

Kirchhoff's Law gives us the derivative equation  If  use Euler's method with step size 0.1 to estimate  after 0.3 second.

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Question 8

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  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).

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Question 9

Solve the differential equation.

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Question 10

Select a direction field for the differential equation  from a set of direction fields labeled I-IV.

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Question 11

Solve the initial-value problem.

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Question 12

A tank contains  of brine with  of dissolved salt.Pure water enters the tank at a rate of  The solution is kept thoroughly mixed and drains from the tank at the same rate.How much salt is in the tank after

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Question 13

A phase trajectory is shown for populations of rabbits  and foxes  Describe how each population changes as time goes by.  Select the correct statement.

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Question 14

Determine whether the differential equation is linear.

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Question 15

Consider the differential equation  as a model for a fish population, where  is measured in weeks and  is a constant.For what values of does the fish population always die out?

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Question 16

Which equation does the function  satisfy?

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Question 17

Solve the differential equation.

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Question 18

Find the solution of the differential equation that satisfies the initial condition

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Question 19

Let  What are the equilibrium solutions?

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Question 20

A function  satisfies the differential equation  What are the constant solutions of the equation?

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Quiz 9: Differential Equations

A population is modeled by the differential equation For what values of is the population decreasing?

Determine whether the differential equation is linear.

Solve the differential equation.

Find the solution of the initial-value problem and use it to find the population when

Find the solution of the differential equation hat satisfies the initial condition

Kirchhoff's Law gives us the derivative equation If use Euler's method with step size 0.1 to estimate after 0.3 second.

Solve the differential equation.

Select a direction field for the differential equation from a set of direction fields labeled I-IV.

Solve the initial-value problem.

A tank contains of brine with of dissolved salt.Pure water enters the tank at a rate of The solution is kept thoroughly mixed and drains from the tank at the same rate.How much salt is in the tank after

A phase trajectory is shown for populations of rabbits and foxes Describe how each population changes as time goes by. Select the correct statement.

Determine whether the differential equation is linear.

Consider the differential equation as a model for a fish population, where is measured in weeks and is a constant.For what values of does the fish population always die out?

Which equation does the function satisfy?

Solve the differential equation.

Find the solution of the differential equation that satisfies the initial condition

Let What are the equilibrium solutions?

A function satisfies the differential equation What are the constant solutions of the equation?