Question 1

Select the correct Answer: for each question.
-We modeled populations of aphids and ladybugs with a Lotka-Volterra system.Suppose we modify those equations as follows:   Find the equilibrium solution.

Accepted Answer

A)   
B)   
C)   
D)   
E)    D

Question 2

Suppose that a population develops according to the logistic equation  where  is measured in weeks.What is the carrying capacity?

Accepted Answer

A)   
B)   
C)   
D)   
E)    A

Question 3

Solve the differential equation.

Accepted Answer

The answer of Solve the differential equation. ...

Question 4

Solve the differential equation.

Accepted Answer

The answer of Solve the differential equation. ...

Question 5

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

Accepted Answer

The answer of Find the solution of the differential equation...

Question 6

Solve the initial-value problem.

Accepted Answer

The answer of Solve the initial-value problem. ...

Question 7

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

Accepted Answer

The answer of A phase trajectory is shown for populations...

Question 8

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

Accepted Answer

The answer of A tank contains  of brine with...

Question 9

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

Accepted Answer

The answer of Find the solution of the differential equation...

Question 10

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 yourAnswer in billions to one decimal place.(Because the initial population is small compared to the carrying capacity, you can take  to be an estimate of the initial relative growth rate.) Select the correct Answer

Accepted Answer

A)  78.3 billion
B)  27.0 billion
C)  17.1 billion
D)  59.2 billion
E)  32.9 billion

Question 11

Find the orthogonal trajectories of the family of curves.

Accepted Answer

The answer of Find the orthogonal trajectories of the family...

Question 12

be a positive number.A differential equation of the form  where  is a positive constant is called  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? Select the correct Answer

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 13

Select the correct Answer: for each question.
-A common inhabitant of human intestines is the bacterium  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.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 14

A sum of  is invested at  interest.If  is the amount of the investment at time  for the case of continuous compounding, write a differential equation and an initial condition satisfied by

Accepted Answer

The answer of A sum of  is invested at...

Question 15

Suppose that a population develops according to the logistic equation  where  is measured in weeks.What is the carrying capacity?

Accepted Answer

The answer of Suppose that a population develops according to...

Question 16

An object with mass  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  is a positive constant, and Newton's Second Law gives  Find the limiting velocity.

Accepted Answer

The answer of An object with mass  is dropped...

Question 17

Select the correct Answer: for each question.
-Solve the differential equation.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 18

Let  What are the equilibrium solutions?

Accepted Answer

The answer of Let  What are the equilibrium solutions?...

Question 19

Select the correct Answer: for each question.
-Which of the following functions are the constant solutions of the equation  
a.  
b.  
c.  
d.  
e.

Accepted Answer

The answer of Select the correct Answer: for each question.
-Which...

Question 20

Solve the initial-value problem.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Exam 9: Differential Equations

Select the correct Answer: for each question. -We modeled populations of aphids and ladybugs with a Lotka-Volterra system.Suppose we modify those equations as follows: Find the equilibrium solution.

Suppose that a population develops according to the logistic equation where is measured in weeks.What is the carrying capacity?

Solve the differential equation.

Solve the differential equation.

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

Solve the initial-value problem.

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 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

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

Find the orthogonal trajectories of the family of curves.

Select the correct Answer: for each question. -A common inhabitant of human intestines is the bacterium 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 sum of is invested at interest.If is the amount of the investment at time for the case of continuous compounding, write a differential equation and an initial condition satisfied by

Suppose that a population develops according to the logistic equation where is measured in weeks.What is the carrying capacity?

Select the correct Answer: for each question. -Solve the differential equation.

Let What are the equilibrium solutions?

Select the correct Answer: for each question. -Which of the following functions are the constant solutions of the equation a. b. c. d. e.

Solve the initial-value problem.