Question 1

Solve the differential equation   .

Accepted Answer

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

Question 2

Find   if   ..

Accepted Answer

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

Question 3

The table lists the approximate value V of a mid-sized sedan for the years 2003 through 2009. The variable t represents the time in years, with   corresponding to 2003. Use the regression capabilities of a graphing utility to fit an exponential model to the data. Round all numerical values in your answer to four decimal places. Your answer may be slightly different depending on the number of digits your graphing utility uses in computations.

Accepted Answer

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

Question 4

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) 6,174.815 
B) 6,224.815 
C) 382.187 
D) 6,254.815 
E) 168,070.000 
A) 6,174.815 
B) 6,224.815 
C) 382.187 
D) 6,254.815 
E) 168,070.000

Question 5

Evaluate the definite integral   .

Accepted Answer

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

Question 6

Suppose a population of bacteria is changing at a rate of   where t is the time in days. The initial population (when t = 0) is 1000. Write an equation that gives the population at any time t.

Accepted Answer

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

Question 7

Suppose the term of a mortgage t (in years) can be approximated by   where x is the monthly payment in dollars. Use the model to approximate the term of a home mortgage for which the monthly payment is   . What is the total amount paid? Round your answer to the nearest cent. Your answer may be slightly different depending on the number of digits your technology uses in computations.

Accepted Answer

A) $1284.55 
B) $308,293.13 
C) $15,414.66 
D) $51,382.19 
E) $616,586.26 
A) $1284.55 
B) $308,293.13 
C) $15,414.66 
D) $51,382.19 
E) $616,586.26

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 2014. Round your answer to two decimal places.

Accepted Answer

A) 7.93 million 
B) 7.74 million 
C) 8.12 million 
D) 6.86 million 
E) 7.03 million 
A) 7.93 million 
B) 7.74 million 
C) 8.12 million 
D) 6.86 million 
E) 7.03 million

Question 9

Find the derivative of the function   .

Accepted Answer

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

Question 10

Find the indefinite integral of   .

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E)

Question 11

Find the indefinite integral.

Accepted Answer

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E)    
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E)

Question 12

Evaluate the definite integral.

Accepted Answer

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E)    
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E)

Question 13

Use logarithmic differentiation to find the derivative of   .

Accepted Answer

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E)    
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E)

Question 14

Suppose the table below shows the temperature   at which a given liquid boils at selected pressures p (pounds per square inch). A model that approximates the data is   . Find the rate of change of T with respect to p when   . Round your answer to two decimal places.p51014.696(1 atm)2030406080100T327.43404.29448.84485.71536.18573.59629.02670.61704.38

Accepted Answer

A) 5.34   
B) 4.25   
C) 152.22   
D) 153.31   
E) 1.09   
A) 5.34   
B) 4.25   
C) 152.22   
D) 153.31   
E) 1.09

Question 15

Use implicit differentiation to find   .

Accepted Answer

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

Question 16

Use implicit differentiation to find   .

Accepted Answer

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D)    
E)    
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B)    
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E)

Question 17

Find the indefinite integral.

Accepted Answer

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E)    
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E)

Question 18

Find   .

Accepted Answer

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E)    
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E)

Question 19

Find the derivative of the function   .

Accepted Answer

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

Question 20

Solve the differential equation.

Accepted Answer

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

Solve the differential equation .

Find if ..

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.

Evaluate the definite integral .

Suppose a population of bacteria is changing at a rate of where t is the time in days. The initial population (when t = 0) is 1000. Write an equation that gives the population at any time t.

Find the derivative of the function .

Find the indefinite integral of .

Find the indefinite integral.

Evaluate the definite integral.

Use logarithmic differentiation to find the derivative of .

Use implicit differentiation to find .

Use implicit differentiation to find .

Find the indefinite integral.

Find .

Find the derivative of the function .

Solve the differential equation.

Prerequisites

Functions and Their Graphs

Polynomial and Rational Functions

Limits and Their Properties

Differentiation

Applications of Differentiation

Integration

Exponential and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Trigonometric Functions and Calculus

Topics in Analytic Geometry

Additional Topics in Trigonometry

Filters

Exam 9: Exponential and Logarithmic Functions and Calculus

Solve the differential equation .

Find if ..

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.

Evaluate the definite integral .

Suppose a population of bacteria is changing at a rate of where t is the time in days. The initial population (when t = 0) is 1000. Write an equation that gives the population at any time t.

Find the derivative of the function .

Find the indefinite integral of .

Find the indefinite integral.

Evaluate the definite integral.

Use logarithmic differentiation to find the derivative of .

Use implicit differentiation to find .

Use implicit differentiation to find .

Find the indefinite integral.

Find .

Find the derivative of the function .

Solve the differential equation.

Prerequisites

Functions and Their Graphs

Polynomial and Rational Functions

Limits and Their Properties

Differentiation

Applications of Differentiation

Integration

Exponential and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Trigonometric Functions and Calculus

Topics in Analytic Geometry

Additional Topics in Trigonometry

Filters