Question 1

Write   as a single logarithm with a coefficient of 1. Assume all variable expressions represent positive real numbers.

Accepted Answer

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

Question 2

Find the inverse function informally   Verify that   and

Accepted Answer

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

Question 3

The average monthly sales   (in billions of dollars) in retail trade in the United States from 1996 to 2005 can be approximated by the model     where   represents the year, with   corresponding to 1996.Estimate the year in which the average monthly sales first exceeded $330 billion.

Accepted Answer

A)  2003 
B)  2004 
C)  2002 
D)  1999 
E)  1997 
A)  2003 
B)  2004 
C)  2002 
D)  1999 
E)  1997

Question 4

Use the functions given by   and   to find the composition of functions

Accepted Answer

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

Question 5

Apply the Inverse Property of logarithmic or exponential functions to simplify the expression below.

Accepted Answer

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

Question 6

Solve for

Accepted Answer

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

Question 7

Use a calculator to evaluate   Round your result to three decimal places.

Accepted Answer

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

Question 8

Rewrite the logarithmic equation   in exponential form.

Accepted Answer

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

Question 9

Find the domain of the function

Accepted Answer

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

Question 10

Approximate the solution of   to 3 decimal places.(You may use a graphing utility.)

Accepted Answer

A)  -3.329 
B)  -0.299 
C)  -1.427 
D)  -0.986 
E)  -0.110 
A)  -3.329 
B)  -0.299 
C)  -1.427 
D)  -0.986 
E)  -0.110

Question 11

How long will it take $10,000 to quadruple if it is invested in a savings account that pays 5.5% annual interest compounded continuously? Round to the nearest year.

Accepted Answer

A)  25 years 
B)  20 years 
C)  19 years 
D)  32 years 
E)  30 years 
A)  25 years 
B)  20 years 
C)  19 years 
D)  32 years 
E)  30 years

Question 12

Find the vertical asymptote of the logarithmic function below.

Accepted Answer

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

Question 13

Evaluate the expression below.Round your results to three decimal places.

Accepted Answer

A)  0.135 
B)  0.018 
C)  54.598 
D)  0.050 
E)  0.007 
A)  0.135 
B)  0.018 
C)  54.598 
D)  0.050 
E)  0.007

Question 14

Solve for x:   Round to 3 decimal places.

Accepted Answer

A)  1.407 
B)  0.407 
C)  1.362 
D)  -1.362 
E)  no solution 
A)  1.407 
B)  0.407 
C)  1.362 
D)  -1.362 
E)  no solution

Question 15

You take a three-pound package of steaks out of the freezer at 11 A.M.and place it in the refrigerator.Assume that the refrigerator temperature is   and that the freezer temperature is   Use the formula for Newton's Law of Cooling   where   is the time in hours (with   corresponding to 12 P.M.) and   is the temperature of the package of steaks (in degrees Fahrenheit).Find the time when the steaks will thaw (or reach   ).

Accepted Answer

A)  3:51 P.M. 
B)  4:31 P.M. 
C)  5:41 P.M. 
D)  7:01 P.M. 
E)  6:11 P.M. 
A)  3:51 P.M. 
B)  4:31 P.M. 
C)  5:41 P.M. 
D)  7:01 P.M. 
E)  6:11 P.M.

Question 16

The table below shows the cost   (in millions of dollars) of a 30-second ad during the Super Bowl for several years from 1987 to 2006.   Use the regression feature of a graphing utility to find an exponential model for the data.Predict the cost of a 30-second ad during the Super Bowl in 2012.Round to the nearest ten thousand.

Accepted Answer

A)  $4.29 million 
B)  $5.01 million 
C)  $5.86 million 
D)  $4.64 million 
E)  $3.67 million 
A)  $4.29 million 
B)  $5.01 million 
C)  $5.86 million 
D)  $4.64 million 
E)  $3.67 million

Question 17

Approximate the solution to   Round to 3 decimal places.

Accepted Answer

A)  -0.632 
B)  0.500 
C)  0.582 
D)  2.718 
E)  0.111 
A)  -0.632 
B)  0.500 
C)  0.582 
D)  2.718 
E)  0.111

Question 18

Sketch the graph of the function

Accepted Answer

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

Question 19

The number of certain type of bacteria increases according to the model   where t is time (in hours) 
a.Find P(0).
B.Find P(5).
C.Find P(10).
D.Find P(24).

Accepted Answer

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

Question 20

Use the functions given by   and   to find the value

Accepted Answer

A)  1 
B)  0 
C)  3 
D)  4 
E)  2 
A)  1 
B)  0 
C)  3 
D)  4 
E)  2

Write as a single logarithm with a coefficient of 1. Assume all variable expressions represent positive real numbers.

Find the inverse function informally Verify that and

The average monthly sales (in billions of dollars) in retail trade in the United States from 1996 to 2005 can be approximated by the model where represents the year, with corresponding to 1996.Estimate the year in which the average monthly sales first exceeded $330 billion.

Use the functions given by and to find the composition of functions

Apply the Inverse Property of logarithmic or exponential functions to simplify the expression below.

Solve for

Use a calculator to evaluate Round your result to three decimal places.

Rewrite the logarithmic equation in exponential form.

Find the domain of the function

Approximate the solution of to 3 decimal places.(You may use a graphing utility.)

How long will it take $10,000 to quadruple if it is invested in a savings account that pays 5.5% annual interest compounded continuously? Round to the nearest year.

Find the vertical asymptote of the logarithmic function below.

Evaluate the expression below.Round your results to three decimal places.

Solve for x: Round to 3 decimal places.

Approximate the solution to Round to 3 decimal places.

Sketch the graph of the function

The number of certain type of bacteria increases according to the model where t is time (in hours) a.Find P(0). B.Find P(5). C.Find P(10). D.Find P(24).

Use the functions given by and to find the value

Fundamental Concepts of Algebra

Equations and Inequalities

Functions and Graphs

Polynomial and Rational Functions

Systems of Equations and Inequalities

Matrices and Determinants

Sequences, Series, and Probability

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Exam 4: Exponential and Logarithmic Functions

Write as a single logarithm with a coefficient of 1. Assume all variable expressions represent positive real numbers.

Find the inverse function informally Verify that and

The average monthly sales (in billions of dollars) in retail trade in the United States from 1996 to 2005 can be approximated by the model where represents the year, with corresponding to 1996.Estimate the year in which the average monthly sales first exceeded $330 billion.

Use the functions given by and to find the composition of functions

Apply the Inverse Property of logarithmic or exponential functions to simplify the expression below.

Solve for

Use a calculator to evaluate Round your result to three decimal places.

Rewrite the logarithmic equation in exponential form.

Find the domain of the function

Approximate the solution of to 3 decimal places.(You may use a graphing utility.)

How long will it take $10,000 to quadruple if it is invested in a savings account that pays 5.5% annual interest compounded continuously? Round to the nearest year.

Find the vertical asymptote of the logarithmic function below.

Evaluate the expression below.Round your results to three decimal places.

Solve for x: Round to 3 decimal places.

Approximate the solution to Round to 3 decimal places.

Sketch the graph of the function

The number of certain type of bacteria increases according to the model where t is time (in hours) a.Find P(0). B.Find P(5). C.Find P(10). D.Find P(24).

Use the functions given by and to find the value

Fundamental Concepts of Algebra

Equations and Inequalities

Functions and Graphs

Polynomial and Rational Functions

Systems of Equations and Inequalities

Matrices and Determinants

Sequences, Series, and Probability

Filters