Question 1

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 2

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 3

Find the principal that must be invested at the rate 8%,compounded monthly,so that $3,000,000 will be available for retirement in 50 years.Round your answer to the nearest cent. ​

Accepted Answer

A) $750,000.00 
B) $55,681.16 
C) $2,151,973.12 
D) $1,000,000.00 
E) $63,963.69 
A) $750,000.00 
B) $55,681.16 
C) $2,151,973.12 
D) $1,000,000.00 
E) $63,963.69

Question 4

A population of rabbits in a certain habitat grows according to the differential equation   where t is measured in months   and y is measured in hundreds of rabbits.There were initially 100 rabbits in this habitat;that is,   .​ ​
What is the fastest growth rate,in rabbits per month,that this population exhibits?​
​

Accepted Answer

A) ​150 
B) ​600 
C) ​300 
D) ​250 
A) ​150 
B) ​600 
C) ​300 
D) ​250

Question 5

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

Accepted Answer

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

Question 6

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 7

A calf that weighs 75 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

Suppose that the population (in millions)of a Paraguay in 2007 is 6.7 and that expected continuous annual rate of change of the population is 0.024.The exponential growth model for the population by letting   corresponds to 2000 is   .Use the model to predict the population of the country in 2015.Round your answer to two decimal places. ​

Accepted Answer

A) 7.03 million 
B) 7.93 million 
C) 8.32 million 
D) 8.12 million 
E) 6.86 million 
A) 7.03 million 
B) 7.93 million 
C) 8.32 million 
D) 8.12 million 
E) 6.86 million

Question 9

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 10,000 cubic feet of water in the tank,and at time   hours,6,000 cubic feet of water remained. ​
​To the nearest cubic foot,how much water remained in the tank at time   hours?
​

Accepted Answer

A) ​4,937 
B) ​5,170 
C) ​5,394 
D) ​4,891 
A) ​4,937 
B) ​5,170 
C) ​5,394 
D) ​4,891

Question 10

​
A differentiable function   is defined such that,for all values of   in its domain,   .
-​What is the domain of   ?

Accepted Answer

The answer of ​
A differentiable function   is defined...

Question 11

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.Write a logistic function that models the population of panthers in the preserve. ​

Accepted Answer

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

Question 12

​Water is being pumped continuously into a tank at a rate that is inversely proportional to the amount of water in the tank;that is,   ,where y is the number of gallons of water in the tank after t minutes   .Initially there were 5 gallons of water in the tank,and after 3 inutes there were 8 gallons.How many gallons of water were in the tank at time 20 minutes? ​

Accepted Answer

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

Question 13

The half-life of the carbon isotope C-14 is approximately 5,715 years.If the initial quantity of the isotope is 38 g,what is the amount left after 1,000 years? Round your answer to two decimal places. ​

Accepted Answer

A) 33.66 g 
B) 35.76 g 
C) 34.16 g 
D) 3.32 g 
E) 16.83 g 
A) 33.66 g 
B) 35.76 g 
C) 34.16 g 
D) 3.32 g 
E) 16.83 g

Question 14

The initial investment in a savings account in which interest is compounded continuously is $850.If the time required to double the amount is   years,what is the amount after 14 years? Round your answer to the nearest cent. ​

Accepted Answer

A) $3,400.00 
B) $3,099.86 
C) $3,173.33 
D) $2,699.86 
E) $9,197.18 
A) $3,400.00 
B) $3,099.86 
C) $3,173.33 
D) $2,699.86 
E) $9,197.18

Question 15

A calf that weighs 60 pounds at birth gains weight at the rate   where w is weight in pounds and t is time in years.What is the maximum weight of the animal if one uses the model   ? ​

Accepted Answer

A) 1200 lb 
B) 810 lb 
C) 1140 lb 
D) 1260 lb 
E) 1950 lb 
A) 1200 lb 
B) 810 lb 
C) 1140 lb 
D) 1260 lb 
E) 1950 lb

Question 16

​Consider the differential equation   ,for which the solution is g(x). Which of the following statements is true about the particular solution that contains (1,-4)?
​

Accepted Answer

A) ​g(x)is increasing and concave up. 
B) ​g(x)is increasing and concave down. 
C) ​g(x)is decreasing and concave up. 
D) ​g(x)is decreasing and concave down. 
A) ​g(x)is increasing and concave up. 
B) ​g(x)is increasing and concave down. 
C) ​g(x)is decreasing and concave up. 
D) ​g(x)is decreasing and concave down.

Question 17

The initial investment in a savings account in which interest is compounded continuously is $775.If the time required to double the amount is   years,what is the annual rate? Round your answer to two decimal places. ​

Accepted Answer

A) 9.24 % 
B) 9.90 % 
C) 10.82 % 
D) 8.04 % 
E) 10.64 % 
A) 9.24 % 
B) 9.90 % 
C) 10.82 % 
D) 8.04 % 
E) 10.64 %

Question 18

Solve the differential equation. ​   ​

Accepted Answer

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

Question 19

Find the function   passing through the point   with the first derivative   . ​

Accepted Answer

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

Question 20

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

Accepted Answer

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

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

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

Find the principal that must be invested at the rate 8%,compounded monthly,so that $3,000,000 will be available for retirement in 50 years.Round your answer to the nearest cent.

Use integration to find a general 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.

A calf that weighs 75 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 .

A differentiable function is defined such that,for all values of in its domain, . -What is the domain of ?

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.Write a logistic function that models the population of panthers in the preserve.

The half-life of the carbon isotope C-14 is approximately 5,715 years.If the initial quantity of the isotope is 38 g,what is the amount left after 1,000 years? Round your answer to two decimal places.

The initial investment in a savings account in which interest is compounded continuously is $850.If the time required to double the amount is years,what is the amount after 14 years? Round your answer to the nearest cent.

A calf that weighs 60 pounds at birth gains weight at the rate where w is weight in pounds and t is time in years.What is the maximum weight of the animal if one uses the model ?

Consider the differential equation ,for which the solution is g(x). Which of the following statements is true about the particular solution that contains (1,-4)?

The initial investment in a savings account in which interest is compounded continuously is $775.If the time required to double the amount is years,what is the annual rate? Round your answer to two decimal places.

Solve the differential equation.

Find the function passing through the point with the first derivative .

Which of the following is a 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

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

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

Find the principal that must be invested at the rate 8%,compounded monthly,so that $3,000,000 will be available for retirement in 50 years.Round your answer to the nearest cent. ​

Use integration to find a general 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. ​

A calf that weighs 75 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 . ​

​ A differentiable function is defined such that,for all values of in its domain, . -​What is the domain of ?

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.Write a logistic function that models the population of panthers in the preserve. ​

The half-life of the carbon isotope C-14 is approximately 5,715 years.If the initial quantity of the isotope is 38 g,what is the amount left after 1,000 years? Round your answer to two decimal places. ​

The initial investment in a savings account in which interest is compounded continuously is $850.If the time required to double the amount is years,what is the amount after 14 years? Round your answer to the nearest cent. ​

A calf that weighs 60 pounds at birth gains weight at the rate where w is weight in pounds and t is time in years.What is the maximum weight of the animal if one uses the model ? ​

​Consider the differential equation ,for which the solution is g(x). Which of the following statements is true about the particular solution that contains (1,-4)? ​

The initial investment in a savings account in which interest is compounded continuously is $775.If the time required to double the amount is years,what is the annual rate? Round your answer to two decimal places. ​

Solve the differential equation. ​ ​

Find the function passing through the point with the first derivative . ​

Which of the following is a 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

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

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

Find the principal that must be invested at the rate 8%,compounded monthly,so that $3,000,000 will be available for retirement in 50 years.Round your answer to the nearest cent.

Use integration to find a general 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.

A calf that weighs 75 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 .

A differentiable function is defined such that,for all values of in its domain, . -What is the domain of ?

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.Write a logistic function that models the population of panthers in the preserve.

The half-life of the carbon isotope C-14 is approximately 5,715 years.If the initial quantity of the isotope is 38 g,what is the amount left after 1,000 years? Round your answer to two decimal places.

The initial investment in a savings account in which interest is compounded continuously is $850.If the time required to double the amount is years,what is the amount after 14 years? Round your answer to the nearest cent.

A calf that weighs 60 pounds at birth gains weight at the rate where w is weight in pounds and t is time in years.What is the maximum weight of the animal if one uses the model ?

Consider the differential equation ,for which the solution is g(x). Which of the following statements is true about the particular solution that contains (1,-4)?

The initial investment in a savings account in which interest is compounded continuously is $775.If the time required to double the amount is years,what is the annual rate? Round your answer to two decimal places.

Solve the differential equation.

Find the function passing through the point with the first derivative .

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