Question 1

Match the logistic equation and initial condition with the graph of the solution. ​   ​

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 2

Find the orthogonal trajectories of the family ​   .
​

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 3

Write and solve the differential equation that models the following verbal statement: ​
The rate of change of   with respect to   is proportional to   .
​

Accepted Answer

A)    ,   
B)    ,   
C)    ,   
D)    ,   
E)    ,   
A)    ,   
B)    ,   
C)    ,   
D)    ,   
E)    ,

Question 4

Which of the following is a solution of the differential equation   ? ​

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 5

A conservation organization releases 30 panthers into a preserve. After 3 years, there are 50 panthers in the preserve. The preserve has a carrying capacity of 150. Determine the population after 6 years. Discard any fractional part of your answer.

Accepted Answer

A)  74 
B)  66 
C)  87 
D)  79 
E)  130 
A)  74 
B)  66 
C)  87 
D)  79 
E)  130

Question 6

The half-life of the carbon isotope C-14 is approximately 5,715 years. If the initial quantity of the isotope is 34 g, what is the amount left after 10,000 years? Round your answer to two decimal places. ​

Accepted Answer

A)  10.11 g 
B)  18.54 g 
C)  10.61 g 
D)  29.75 g 
E)  5.06 g 
A)  10.11 g 
B)  18.54 g 
C)  10.61 g 
D)  29.75 g 
E)  5.06 g

Question 7

A calf that weighs 70 pounds at birth gains weight at the rate   where w is weight in pounds and t is time in years. Use a computer algebra system to solve the differential equation for   . ​

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 8

Assume an object weighing 7 pounds is dropped from a height of 9,000 feet, where the air resistance is proportional to the velocity. Round numerical answers in your answer to two places. ​
(i) Write the velocity as a function of time if the object's velocity after 4 seconds is 2.33 feet per second.
​
(ii) What is the limiting value of the velocity function?
​

Accepted Answer

A)  (i)   ; (ii) 0 
B)  (i)   ; (ii) 0 
C)  (i)   ; (ii) 2.33 
D)  (i)   ; (ii) 2.33 
E)  (i)   ; (ii) limit does not exist 
A)  (i)   ; (ii) 0 
B)  (i)   ; (ii) 0 
C)  (i)   ; (ii) 2.33 
D)  (i)   ; (ii) 2.33 
E)  (i)   ; (ii) limit does not exist

Question 9

Use integration to find a general solution of the differential equation. ​   ​

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 10

A container of hot liquid is placed in a freezer that is kept at a constant temperature of   F. The initial temperature of the liquid is   F. After 4 minutes, the liquid's temperature is   F. How much longer will it take for its temperature to decrease to   F? Round your answer to two decimal places. ​

Accepted Answer

A)  2.93 minutes 
B)  4.39 minutes 
C)  4.88 minutes 
D)  1.95 minutes 
E)  5.37 minutes 
A)  2.93 minutes 
B)  4.39 minutes 
C)  4.88 minutes 
D)  1.95 minutes 
E)  5.37 minutes

Question 11

Find the exponential function   that passes through the two given points. Round your values of C and k to four decimal places. ​   ​

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 12

Use integration to find a general solution of the differential equation. ​   ​

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 13

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

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 14

Use integration to find a general solution of the differential equation ​   ​

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 15

The half-life of the carbon isotope C-14 is approximately 5,715 years. If the amount left after 4,000 years is 1.3 g, what is the amount after 8,000 years? Round your answer to three decimal places. ​

Accepted Answer

A)  0.800 g 
B)  0.628 g 
C)  1.300 g 
D)  0.303 g 
E)  1.601 g 
A)  0.800 g 
B)  0.628 g 
C)  1.300 g 
D)  0.303 g 
E)  1.601 g

Question 16

Solve the first-order linear differential equation   .

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 17

The rate of change of N is proportional to N. When   ,   and when   ,   . What is the value of N when   ? Round your answer to three decimal places. ​

Accepted Answer

A)  1,316.250 
B)  1,286.250 
C)  1,236.250 
D)  140.599 
E)  20,580.000 
A)  1,316.250 
B)  1,286.250 
C)  1,236.250 
D)  140.599 
E)  20,580.000

Question 18

Find the orthogonal trajectories of the family   . ​

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 19

Select from the choices below the slope field for the differential equation. ​   ​

Accepted Answer

A)    
B)    
C)    
D)  none of the above 
A)    
B)    
C)    
D)  none of the above

Question 20

Find the particular solution of the differential equation   passing through the point   .

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Match the logistic equation and initial condition with the graph of the solution.

Find the orthogonal trajectories of the family .

Write and solve the differential equation that models the following verbal statement: The rate of change of with respect to is proportional to .

Which of the following is a solution of the differential equation ?

A conservation organization releases 30 panthers into a preserve. After 3 years, there are 50 panthers in the preserve. The preserve has a carrying capacity of 150. Determine the population after 6 years. Discard any fractional part of your answer.

The half-life of the carbon isotope C-14 is approximately 5,715 years. If the initial quantity of the isotope is 34 g, what is the amount left after 10,000 years? Round your answer to two decimal places.

A calf that weighs 70 pounds at birth gains weight at the rate where w is weight in pounds and t is time in years. Use a computer algebra system to solve the differential equation for .

Use integration to find a general solution of the differential equation.

A container of hot liquid is placed in a freezer that is kept at a constant temperature of F. The initial temperature of the liquid is F. After 4 minutes, the liquid's temperature is F. How much longer will it take for its temperature to decrease to F? Round your answer to two decimal places.

Find the exponential function that passes through the two given points. Round your values of C and k to four decimal places.

Use integration to find a general solution of the differential equation.

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

Use integration to find a general solution of the differential equation

The half-life of the carbon isotope C-14 is approximately 5,715 years. If the amount left after 4,000 years is 1.3 g, what is the amount after 8,000 years? Round your answer to three decimal places.

Solve the first-order linear differential equation .

The rate of change of N is proportional to N. When , and when , . What is the value of N when ? Round your answer to three decimal places.

Find the orthogonal trajectories of the family .

Select from the choices below the slope field for the differential equation.

Find the particular solution of the differential equation passing through the point .

Preparation for Calculus

Limits and Their Properties

Differentiation

Applications of Differentiation

Integration

Applications of Integration

Integration Techniques and Improper Integrals

Infinite Series

Conics, Parametric Equations, and Polar Coordinates

Vectors and the Geometry of Space

Vector-Valued Functions

Functions of Several Variables

Multiple Integration

Vector Anal

Filters

Exam 6: Differential Equations

Match the logistic equation and initial condition with the graph of the solution. ​ ​

Find the orthogonal trajectories of the family ​ . ​

Write and solve the differential equation that models the following verbal statement: ​ The rate of change of with respect to is proportional to . ​

Which of the following is a solution of the differential equation ? ​

A conservation organization releases 30 panthers into a preserve. After 3 years, there are 50 panthers in the preserve. The preserve has a carrying capacity of 150. Determine the population after 6 years. Discard any fractional part of your answer.

The half-life of the carbon isotope C-14 is approximately 5,715 years. If the initial quantity of the isotope is 34 g, what is the amount left after 10,000 years? Round your answer to two decimal places. ​

A calf that weighs 70 pounds at birth gains weight at the rate where w is weight in pounds and t is time in years. Use a computer algebra system to solve the differential equation for . ​

Use integration to find a general solution of the differential equation. ​ ​

A container of hot liquid is placed in a freezer that is kept at a constant temperature of F. The initial temperature of the liquid is F. After 4 minutes, the liquid's temperature is F. How much longer will it take for its temperature to decrease to F? Round your answer to two decimal places. ​

Find the exponential function that passes through the two given points. Round your values of C and k to four decimal places. ​ ​

Use integration to find a general solution of the differential equation. ​ ​

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

Use integration to find a general solution of the differential equation ​ ​

The half-life of the carbon isotope C-14 is approximately 5,715 years. If the amount left after 4,000 years is 1.3 g, what is the amount after 8,000 years? Round your answer to three decimal places. ​

Solve the first-order linear differential equation .

The rate of change of N is proportional to N. When , and when , . What is the value of N when ? Round your answer to three decimal places. ​

Find the orthogonal trajectories of the family . ​

Select from the choices below the slope field for the differential equation. ​ ​

Find the particular solution of the differential equation passing through the point .

Preparation for Calculus

Limits and Their Properties

Differentiation

Applications of Differentiation

Integration

Applications of Integration

Integration Techniques and Improper Integrals

Infinite Series

Conics, Parametric Equations, and Polar Coordinates

Vectors and the Geometry of Space

Vector-Valued Functions

Functions of Several Variables

Multiple Integration

Vector Anal

Filters

Match the logistic equation and initial condition with the graph of the solution.

Find the orthogonal trajectories of the family .

Write and solve the differential equation that models the following verbal statement: The rate of change of with respect to is proportional to .

Which of the following is a solution of the differential equation ?

The half-life of the carbon isotope C-14 is approximately 5,715 years. If the initial quantity of the isotope is 34 g, what is the amount left after 10,000 years? Round your answer to two decimal places.

A calf that weighs 70 pounds at birth gains weight at the rate where w is weight in pounds and t is time in years. Use a computer algebra system to solve the differential equation for .

Use integration to find a general solution of the differential equation.

A container of hot liquid is placed in a freezer that is kept at a constant temperature of F. The initial temperature of the liquid is F. After 4 minutes, the liquid's temperature is F. How much longer will it take for its temperature to decrease to F? Round your answer to two decimal places.

Find the exponential function that passes through the two given points. Round your values of C and k to four decimal places.

Use integration to find a general solution of the differential equation.

Use integration to find a general solution of the differential equation

The half-life of the carbon isotope C-14 is approximately 5,715 years. If the amount left after 4,000 years is 1.3 g, what is the amount after 8,000 years? Round your answer to three decimal places.

The rate of change of N is proportional to N. When , and when , . What is the value of N when ? Round your answer to three decimal places.

Find the orthogonal trajectories of the family .

Select from the choices below the slope field for the differential equation.