Question 1

Find an equation of the graph that passes through the point   and has the slope   . ​

Accepted Answer

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Question 2

Suppose that the population (in millions) of a Uganda in 2007 is 30.3 and that expected continuous annual rate of change of the population is 0.036. The exponential growth model for the population by letting   corresponds to 2000 is   . Use the model to predict the population of the country in 2014. Round your answer to two decimal places. ​

Accepted Answer

A)  32.56 millions 
B)  37.61 millions 
C)  40.41 millions 
D)  38.98 millions 
E)  31.41 millions 
A)  32.56 millions 
B)  37.61 millions 
C)  40.41 millions 
D)  38.98 millions 
E)  31.41 millions

Question 3

Sketch the slope field for the differential equation   and use the slope field to sketch the solution that passes through the point   . ​

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Question 4

Match the logistic equation with its graph. ​   ​

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Question 5

Solve the differential equation. ​   ​

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Question 6

The logistic function   models the growth of a population. Determine when the population reaches   % of the maximum carrying capacity. Round your answer to three decimal places.

Accepted Answer

A)  4.317 
B)  3.000 
C)  0.474 
D)  0.677 
E)  0.301 
A)  4.317 
B)  3.000 
C)  0.474 
D)  0.677 
E)  0.301

Question 7

Suppose that the population (in millions) of Hungary in 2007 was 10 and that the expected continuous annual rate of change of the population is -0.003. Find the exponential growth model   for the population by letting   correspond to 2000. Round your answer to four decimal places. ​

Accepted Answer

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Question 8

Use the differential equation   and its slope field to find the slope at the point   .   ​

Accepted Answer

A)  -8 
B)  -1 
C)  -4 
D)  -16 
E)  8 
A)  -8 
B)  -1 
C)  -4 
D)  -16 
E)  8

Question 9

The isotope   has a half-life of 5,715 years. After 2,000 years, a sample of the isotope is reduced to 2.1 grams. What was the initial size of the sample (in grams)? How much will remain after 20,000 years (i.e., after another 18,000 years)? Round your answers to four decimal places. ​

Accepted Answer

A)  1.8735 g, 0.1656 g 
B)  4.2824 g, 0.3786 g 
C)  2.6765 g, 0.2366 g 
D)  3.7471 g, 0.3313 g 
E)  3.4794 g, 0.3076 g 
A)  1.8735 g, 0.1656 g 
B)  4.2824 g, 0.3786 g 
C)  2.6765 g, 0.2366 g 
D)  3.7471 g, 0.3313 g 
E)  3.4794 g, 0.3076 g

Question 10

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

A)  At   the population of foxes reaches a minimum of about 30. 
B)  At   the number of rabbits rebounds to 500. 
C)  At   the number of foxes reaches a maximum of about 2400. 
A)  At   the population of foxes reaches a minimum of about 30. 
B)  At   the number of rabbits rebounds to 500. 
C)  At   the number of foxes reaches a maximum of about 2400.

Question 11

Solve the first order linear differential equation. ​   ​

Accepted Answer

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Question 12

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

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Question 13

A conservation organization releases     into a preserve. After   years, there are     in the preserve. The preserve has a carrying capacity of   . Write a logistic function that models the population of   in the preserve.

Accepted Answer

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Question 14

Find an equation of the graph that passes through the point   and has the slope   . ​

Accepted Answer

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D)    
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Question 15

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

Accepted Answer

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Question 16

Use   as a integrating factor to find the general solution of the differential equation   . ​

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Question 17

Identify the graph of the logistic function   . ​

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Question 18

A 500-gallon tank is half full of distilled water. At time   , a solution containing 0.5 pound of concentrate per gallon enters the tank at the rate of 11 gallons per minute, and the well-stirred mixture is withdrawn at the rate of 9 gallons per minute. At what time will the tank be full? ​

Accepted Answer

A)  250 minutes 
B)  126 minutes 
C)  125 minutes 
D)  501 minutes 
E)  1000 minutes 
A)  250 minutes 
B)  126 minutes 
C)  125 minutes 
D)  501 minutes 
E)  1000 minutes

Question 19

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

Accepted Answer

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B)    
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Question 20

The logistic function   models the growth of a population. Identify the initial population.

Accepted Answer

A)  6 
B)  8 
C)  3 
D)  24 
E)  2 
A)  6 
B)  8 
C)  3 
D)  24 
E)  2

Find an equation of the graph that passes through the point and has the slope .

Sketch the slope field for the differential equation and use the slope field to sketch the solution that passes through the point .

Match the logistic equation with its graph.

Solve the differential equation.

The logistic function models the growth of a population. Determine when the population reaches % of the maximum carrying capacity. Round your answer to three decimal places.

Suppose that the population (in millions) of Hungary in 2007 was 10 and that the expected continuous annual rate of change of the population is -0.003. Find the exponential growth model for the population by letting correspond to 2000. Round your answer to four decimal places.

Use the differential equation and its slope field to find the slope at the point .

The isotope has a half-life of 5,715 years. After 2,000 years, a sample of the isotope is reduced to 2.1 grams. What was the initial size of the sample (in grams)? How much will remain after 20,000 years (i.e., after another 18,000 years)? Round your answers to four decimal places.

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

Solve the first order linear differential equation.

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

A conservation organization releases into a preserve. After years, there are in the preserve. The preserve has a carrying capacity of . Write a logistic function that models the population of in the preserve.

Find an equation of the graph that passes through the point and has the slope .

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

Use as a integrating factor to find the general solution of the differential equation .

Identify the graph of the logistic function .

A 500-gallon tank is half full of distilled water. At time , a solution containing 0.5 pound of concentrate per gallon enters the tank at the rate of 11 gallons per minute, and the well-stirred mixture is withdrawn at the rate of 9 gallons per minute. At what time will the tank be full?

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

The logistic function models the growth of a population. Identify the initial population.

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

Find an equation of the graph that passes through the point and has the slope . ​

Sketch the slope field for the differential equation and use the slope field to sketch the solution that passes through the point . ​

Match the logistic equation with its graph. ​ ​

Solve the differential equation. ​ ​

The logistic function models the growth of a population. Determine when the population reaches % of the maximum carrying capacity. Round your answer to three decimal places.

Suppose that the population (in millions) of Hungary in 2007 was 10 and that the expected continuous annual rate of change of the population is -0.003. Find the exponential growth model for the population by letting correspond to 2000. Round your answer to four decimal places. ​

Use the differential equation and its slope field to find the slope at the point . ​

The isotope has a half-life of 5,715 years. After 2,000 years, a sample of the isotope is reduced to 2.1 grams. What was the initial size of the sample (in grams)? How much will remain after 20,000 years (i.e., after another 18,000 years)? Round your answers to four decimal places. ​

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

Solve the first order linear differential equation. ​ ​

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

A conservation organization releases into a preserve. After years, there are in the preserve. The preserve has a carrying capacity of . Write a logistic function that models the population of in the preserve.

Find an equation of the graph that passes through the point and has the slope . ​

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

Use as a integrating factor to find the general solution of the differential equation . ​

Identify the graph of the logistic function . ​

A 500-gallon tank is half full of distilled water. At time , a solution containing 0.5 pound of concentrate per gallon enters the tank at the rate of 11 gallons per minute, and the well-stirred mixture is withdrawn at the rate of 9 gallons per minute. At what time will the tank be full? ​

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

The logistic function models the growth of a population. Identify the initial population.

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

Find an equation of the graph that passes through the point and has the slope .

Sketch the slope field for the differential equation and use the slope field to sketch the solution that passes through the point .

Match the logistic equation with its graph.

Solve the differential equation.

Suppose that the population (in millions) of Hungary in 2007 was 10 and that the expected continuous annual rate of change of the population is -0.003. Find the exponential growth model for the population by letting correspond to 2000. Round your answer to four decimal places.

Use the differential equation and its slope field to find the slope at the point .

The isotope has a half-life of 5,715 years. After 2,000 years, a sample of the isotope is reduced to 2.1 grams. What was the initial size of the sample (in grams)? How much will remain after 20,000 years (i.e., after another 18,000 years)? Round your answers to four decimal places.

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

Solve the first order linear differential equation.

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

Find an equation of the graph that passes through the point and has the slope .

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

Use as a integrating factor to find the general solution of the differential equation .

Identify the graph of the logistic function .

A 500-gallon tank is half full of distilled water. At time , a solution containing 0.5 pound of concentrate per gallon enters the tank at the rate of 11 gallons per minute, and the well-stirred mixture is withdrawn at the rate of 9 gallons per minute. At what time will the tank be full?

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