Question 1

The deer population, P, in an area is increasing at a rate of 25% per year due to breeding. At the same time, about 200 deer are shot by hunters each year. Which is the differential equation for the population of deer as a function of time t, in years?

Accepted Answer

A)   
B)   
C)   
D)

Question 2

At time t = 0, there are 500 students in a school, 5 of whom have the flu. No one else has been exposed yet. Using the SIR model and the differential equation  , will the flu spread?

Accepted Answer

The answer of At time t = 0, there are...

Question 3

For the strain of the flu modeled by the differential equations   ,
does the disease spread if initially  ?

Accepted Answer

The answer of For the strain of the flu modeled...

Question 4

A spherical raindrop evaporates at a rate proportional to its surface area. If V = volume of the raindrop and S = surface area, which of the following is a differential equation for  ?

Accepted Answer

A)   with k a negative constant 
B)   with k a negative constant 
C)   with k a positive constant 
D)   with k a positive constant

Question 5

Which of the following give a solution to the differential equation  ? Select all that apply. first one:  second one:

Accepted Answer

A) first one 
B) second one 
C) neither

Question 6

A population of birds introduced onto an island without predators grows at a rate proportional to the size of the population. Write a differential equation for the size of the population, P, as a function of time. Is the constant of proportionality positive or negative?

Accepted Answer

A)   , positive 
B)   , negative 
C)   , negative 
D)   , positive

Question 7

The general solution for the differential equation  is

Accepted Answer

A)   
B)   
C)   
D)

Question 8

Find the particular solution to the differential equation  when  .

Accepted Answer

A)   
B)   
C)   
D)

Question 9

Water runs down a certain type of drainpipe at a rate proportional to the amount of water on the roof after a rainfall. Write a differential equation for the amount of water, W, on the roof at time t minutes after the rain stops.

Accepted Answer

A)   
B)   
C)    
D)

Question 10

At time t = 0, there are 300 students at a school, 3 of whom have the flu. Given the differential equation  , will the flu spread?

Accepted Answer

The answer of At time t = 0, there are...

Question 11

A quantity T satisfies the differential equation  .
a) Is T increasing or decreasing when T = -5?
b) For what value of T is the rate of change of T equal to zero?

Accepted Answer

The answer of A quantity T satisfies the differential equation...

Question 12

At time t = 0, there are 700 students in a school, 5 of whom have the flu. No one else has been exposed yet. Using the SIR model,  = _____ and  = _____.

Accepted Answer

The answer of At time t = 0, there are...

Question 13

A population of rodents grows at a rate proportional to the size of the population. Which of the following is the the differential equation for the size of the population, P, as a function of time, t?

Accepted Answer

A)   , with k positive 
B)   , with k negative 
C)   , with k positive 
D)   , with k negative

Question 14

Elk and buffalo are in competition with each other. Each would do fine without the other. Which (if any) of the following systems of differential equations could model the interaction between elk and buffalo, with either species being x or y? Select all that apply.

Accepted Answer

A)   ,  
B)   ,  
C)   ,  
D) None of these

Question 15

Find a solution to the differential equation  subject to the initial condition Q = 60 when t = 0.

Accepted Answer

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

Question 16

Does  satisfy  ?

Accepted Answer

The answer of Does  satisfy  ?...

Question 17

If  is a solution to the differential equation  and y = 20 when t = 0, then k = _____ and C = _____.

Accepted Answer

The answer of If  is a solution to the...

Question 18

Trout are introduced into a stream. Trout is a predator species and therefore has an influence on the population size of other fish. The following figure shows how the trout and other fish populations vary over time. The progress of time is shown by the direction of the arrow. What happens to the size of the trout population at point P?

Accepted Answer

A) It will be stable. 
B) It will be at a maximum. 
C) It will be at a minimum. 
D) Nothing can be determined.

Question 19

The body of a murder victim is found at 9:00 in the morning in a 70  F room. The temperature of the body when it is found is 87  F, and one hour later it is 80  F. If the victim had a normal temperature of 98.6  F when he died, how many hours had the victim been dead when the body was found? Round your answer to one decimal place.

Accepted Answer

The answer of The body of a murder victim is...

Question 20

Which of the following graphs best describes the population of a species that is introduced to a confined space?
I.  II.  III.  IV.

Accepted Answer

The answer of Which of the following graphs best describes...

Exam 9: Mathematical Modeling Using Differential Equations

The deer population, P, in an area is increasing at a rate of 25% per year due to breeding. At the same time, about 200 deer are shot by hunters each year. Which is the differential equation for the population of deer as a function of time t, in years?

At time t = 0, there are 500 students in a school, 5 of whom have the flu. No one else has been exposed yet. Using the SIR model and the differential equation , will the flu spread?

For the strain of the flu modeled by the differential equations , does the disease spread if initially ?

A spherical raindrop evaporates at a rate proportional to its surface area. If V = volume of the raindrop and S = surface area, which of the following is a differential equation for ?

Which of the following give a solution to the differential equation ? Select all that apply. first one: second one:

A population of birds introduced onto an island without predators grows at a rate proportional to the size of the population. Write a differential equation for the size of the population, P, as a function of time. Is the constant of proportionality positive or negative?

The general solution for the differential equation is

Find the particular solution to the differential equation when .

Water runs down a certain type of drainpipe at a rate proportional to the amount of water on the roof after a rainfall. Write a differential equation for the amount of water, W, on the roof at time t minutes after the rain stops.

At time t = 0, there are 300 students at a school, 3 of whom have the flu. Given the differential equation , will the flu spread?

A quantity T satisfies the differential equation . a) Is T increasing or decreasing when T = -5? b) For what value of T is the rate of change of T equal to zero?

At time t = 0, there are 700 students in a school, 5 of whom have the flu. No one else has been exposed yet. Using the SIR model, = _ and = _.

A population of rodents grows at a rate proportional to the size of the population. Which of the following is the the differential equation for the size of the population, P, as a function of time, t?

Elk and buffalo are in competition with each other. Each would do fine without the other. Which (if any) of the following systems of differential equations could model the interaction between elk and buffalo, with either species being x or y? Select all that apply.

Find a solution to the differential equation subject to the initial condition Q = 60 when t = 0.

Does satisfy ?

If is a solution to the differential equation and y = 20 when t = 0, then k = _ and C = _.

Which of the following graphs best describes the population of a species that is introduced to a confined space? I. II. III. IV.