Question 1

Use Euler's Method to make a table of values for the approximate solution of the following differential equation with specified initial value.Use 5 steps of size 0.15. ​   ​

Accepted Answer

A) ​
 
0)000
1)000
2)000
3)000
4)000
5)000

​​ 
B) ​
 
0)000
1)000
2)000
3)000
4)000
5)000

​​ 
C) ​
 
0)000
1)000
2)000
3)000
4)000
5)000

​​ 
D) ​
 
0)000
1)000
2)000
3)000
4)000
5)000

​​ 
E) ​
 
0)000
1)000
2)000
3)000
4)000
5)000

​​ 
A) ​
 
0)000
1)000
2)000
3)000
4)000
5)000

​​ 
B) ​
 
0)000
1)000
2)000
3)000
4)000
5)000

​​ 
C) ​
 
0)000
1)000
2)000
3)000
4)000
5)000

​​ 
D) ​
 
0)000
1)000
2)000
3)000
4)000
5)000

​​ 
E) ​
 
0)000
1)000
2)000
3)000
4)000
5)000

​​

Question 2

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 3

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

Accepted Answer

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

Question 4

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

Accepted Answer

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

Question 5

Find an equation of the graph that passes through the point (2,5)and has the slope   . ​

Accepted Answer

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

Question 6

Sketch the slope field for the differential equation   and use the slope field to sketch the solution satisfying the condition   . ​

Accepted Answer

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

Question 7

Identify the graph of the logistic function   . ​

Accepted Answer

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

Question 8

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

Accepted Answer

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

Question 9

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

Accepted Answer

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

Question 10

For what value(s)of ​x is   ?​

Accepted Answer

The answer of For what value(s)of ​x is  ...

Question 11

Water flows continuously from a large tank at a rate proportional to the amount of water remaining in the tank;that is,   .There was initially 9,000 cubic feet of water in the tank,and at time   hours,8,000 cubic feet of water remained. ​
What is the value of k in the equation   ? Round your answer to 3 decimal places.
​

Accepted Answer

A) ​0.014 
B) ​0.060 
C) ​-0.131 
D) ​-0.059 
A) ​0.014 
B) ​0.060 
C) ​-0.131 
D) ​-0.059

Question 12

The logistic function   models the growth of a population.Identify the maximum carrying capacity. ​

Accepted Answer

A) 15 
B) 5.5 
C) 5 
D) 4 
E) 6 
A) 15 
B) 5.5 
C) 5 
D) 4 
E) 6

Question 13

Find the general solution of the differential equation   . ​

Accepted Answer

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

Question 14

The isotope   has a half-life of 24,100 years.After 1,000 years,a sample of the isotope is reduced to 1.4 grams.What was the initial size of the sample (in grams)? How much will remain after 10,000 years (i.e. ,after another 9,000 years)? Round your answers to four decimal places. ​

Accepted Answer

A) 1.0086 g,0.7565 g 
B) 2.3054 g,1.7291 g 
C) 1.4409 g,1.0807 g 
D) 2.0172 g,1.5130 g 
E) 1.8731 g,1.4049 g 
A) 1.0086 g,0.7565 g 
B) 2.3054 g,1.7291 g 
C) 1.4409 g,1.0807 g 
D) 2.0172 g,1.5130 g 
E) 1.8731 g,1.4049 g

Question 15

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

Accepted Answer

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

Question 16

Each of the following graphs is from a logistic function   .Which one has the largest value of b? ​

Accepted Answer

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

Question 17

The isotope   has a half-life of 5,715 years.After 20,000 years,a sample of the isotope is reduced 0.7 grams.What was the initial size of the sample (in grams)? How large was the sample after the first 2,000 years? Round your answers to four decimal places. ​

Accepted Answer

A) 7.9172 g,6.2119 g 
B) 10.2924 g,8.0755 g 
C) 4.7503 g,3.7271 g 
D) 6.3338 g,4.9695 g 
E) 3.9586 g,3.1059 g 
A) 7.9172 g,6.2119 g 
B) 10.2924 g,8.0755 g 
C) 4.7503 g,3.7271 g 
D) 6.3338 g,4.9695 g 
E) 3.9586 g,3.1059 g

Question 18

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

Accepted Answer

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

Question 19

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) 1,736.667 
B) 1,706.667 
C) 1,656.667 
D) 59.112 
E) 5,120.000 
A) 1,736.667 
B) 1,706.667 
C) 1,656.667 
D) 59.112 
E) 5,120.000

Question 20

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

Accepted Answer

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

Use Euler's Method to make a table of values for the approximate solution of the following differential equation with specified initial value.Use 5 steps of size 0.15.

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

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

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

Find an equation of the graph that passes through the point (2,5)and has the slope .

Sketch the slope field for the differential equation and use the slope field to sketch the solution satisfying the condition .

Identify the graph of the logistic function .

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

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

For what value(s)of x is ?

The logistic function models the growth of a population.Identify the maximum carrying capacity.

Find the general solution of the differential equation .

The isotope has a half-life of 24,100 years.After 1,000 years,a sample of the isotope is reduced to 1.4 grams.What was the initial size of the sample (in grams)? How much will remain after 10,000 years (i.e. ,after another 9,000 years)? Round your answers to four decimal places.

Use integration to find a general solution of the differential equation

Each of the following graphs is from a logistic function .Which one has the largest value of b?

The isotope has a half-life of 5,715 years.After 20,000 years,a sample of the isotope is reduced 0.7 grams.What was the initial size of the sample (in grams)? How large was the sample after the first 2,000 years? Round your answers to four decimal places.

Use integration to find a general solution of the 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.

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

Preparation for Calculus

Limits and Their Properties

Differentiation

Applications of Differentiation

Integration

Applications of Integration

Integration Techniques, L'Hôpital's Rule, and Improper Integrals

Infinite Series

Parametric Equations, Polar Coordinates, and Vectors

Mechanical Ventilation and Sedation: Assessment, Medications, and Complications

Filters

Exam 6: Differential Equations

Use Euler's Method to make a table of values for the approximate solution of the following differential equation with specified initial value.Use 5 steps of size 0.15. ​ ​

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

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

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

Find an equation of the graph that passes through the point (2,5)and has the slope . ​

Sketch the slope field for the differential equation and use the slope field to sketch the solution satisfying the condition . ​

Identify the graph of the logistic function . ​

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

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

For what value(s)of ​x is ?​

The logistic function models the growth of a population.Identify the maximum carrying capacity. ​

Find the general solution of the differential equation . ​

The isotope has a half-life of 24,100 years.After 1,000 years,a sample of the isotope is reduced to 1.4 grams.What was the initial size of the sample (in grams)? How much will remain after 10,000 years (i.e. ,after another 9,000 years)? Round your answers to four decimal places. ​

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

Each of the following graphs is from a logistic function .Which one has the largest value of b? ​

The isotope has a half-life of 5,715 years.After 20,000 years,a sample of the isotope is reduced 0.7 grams.What was the initial size of the sample (in grams)? How large was the sample after the first 2,000 years? Round your answers to four decimal places. ​

Use integration to find a general solution of the 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. ​

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

Preparation for Calculus

Limits and Their Properties

Differentiation

Applications of Differentiation

Integration

Applications of Integration

Integration Techniques, L'Hôpital's Rule, and Improper Integrals

Infinite Series

Parametric Equations, Polar Coordinates, and Vectors

Mechanical Ventilation and Sedation: Assessment, Medications, and Complications

Filters

Use Euler's Method to make a table of values for the approximate solution of the following differential equation with specified initial value.Use 5 steps of size 0.15.

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

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

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

Find an equation of the graph that passes through the point (2,5)and has the slope .

Sketch the slope field for the differential equation and use the slope field to sketch the solution satisfying the condition .

Identify the graph of the logistic function .

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

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

For what value(s)of x is ?

The logistic function models the growth of a population.Identify the maximum carrying capacity.

Find the general solution of the differential equation .

The isotope has a half-life of 24,100 years.After 1,000 years,a sample of the isotope is reduced to 1.4 grams.What was the initial size of the sample (in grams)? How much will remain after 10,000 years (i.e. ,after another 9,000 years)? Round your answers to four decimal places.

Use integration to find a general solution of the differential equation

Each of the following graphs is from a logistic function .Which one has the largest value of b?

The isotope has a half-life of 5,715 years.After 20,000 years,a sample of the isotope is reduced 0.7 grams.What was the initial size of the sample (in grams)? How large was the sample after the first 2,000 years? Round your answers to four decimal places.

Use integration to find a general solution of the 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.

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