Question 1

If the total cost (in dollars) for x units of a product is given by   , what is the total cost of producing 180 units? Round your answer to the nearest cent. ​

Accepted Answer

A) $3462.85 
B) $3262.85 
C) $4195.58 
D) $4066.18 
E) $3442.85 
A) $3462.85 
B) $3262.85 
C) $4195.58 
D) $4066.18 
E) $3442.85

Question 2

Write the expression as the sum or difference of two logarithmic functions containing no exponents. ​   ​

Accepted Answer

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

Question 3

Let   . Use a graphing utility to graph the functions   and   where   . Identify the graphs of   and   below. ​

Accepted Answer

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

Question 4

Use properties of logarithms or a definition to simplify the expression. Check the result with a change-of-base formula and a calculator. Round your answer two decimal places.   ​

Accepted Answer

A) 7.39 
B) 2.00 
C) 4.00 
D) 8.00 
E) no solution 
A) 7.39 
B) 2.00 
C) 4.00 
D) 8.00 
E) no solution

Question 5

The following table gives the average number of students per computer in public schools for the school years that ended in 1985 through 2002. Let x be the number of years past 1980. Find an exponential model for these data. Round your answer to three decimal places. ​   Source: Quality Education Data, Inc., Denver, Colorado
​

Accepted Answer

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

Question 6

Use the following information. Chemists use the pH (hydrogen potential) of a solution to measure its acidity or basicity. The pH is given by the formula   , where   is the concentration of hydrogen ions in moles per liter. What value of   is associated with pH level 13? ​

Accepted Answer

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

Question 7

Let   . Using a graphing utility, graph   for ​   and   . What effect does c have on the graphs?
​

Accepted Answer

A) As c changes, the graph is shifted horizontally by c units. 
B) As c changes, the graph is shifted vertically by c units. 
C) As c changes, the y-intercept and the horizontal asymptote change. 
D) As c changes, the graph is rotated c degrees. 
E) As c changes, the graph is reflected over the line  
) 
A) As c changes, the graph is shifted horizontally by c units. 
B) As c changes, the graph is shifted vertically by c units. 
C) As c changes, the y-intercept and the horizontal asymptote change. 
D) As c changes, the graph is rotated c degrees. 
E) As c changes, the graph is reflected over the line  
)

Question 8

Between the years 1960 and 2002, the percent of women in the work force is given by   , where x is the number of years past 1950 (Source: U.S. Bureau of Labor Statistics). What does this model estimate to be the percent of women in the work force in 2019? Round your answer to two decimal places. ​

Accepted Answer

A) 64.24 
B) 61.69 
C) 66.61 
D) 75.71 
E) 51.70 
A) 64.24 
B) 61.69 
C) 66.61 
D) 75.71 
E) 51.70

Question 9

Evaluate the logarithm by using properties of logarithms and the following facts. Round your answer to two decimal places. ​   ​   ​

Accepted Answer

A) 1.33 
B) 9.72 
C) 1.29 
D) 0.90 
E) 6.30 
A) 1.33 
B) 9.72 
C) 1.29 
D) 0.90 
E) 6.30

Question 10

Pollution levels in Lake Erie have been modeled by the equation   , where x is the volume of pollutants (in cubic kilometers) and t is the time (in years) (Adapted from R. H. Rainey, Science 155 (1967), 1242-1243). Find the initial pollution level; that is, find x when   . ​

Accepted Answer

A) 0.23 km3 
B) 0.1 km3 
C) 0.40 km3 
D) 0.20 km3 
E) 0.7 km3 
A) 0.23 km3 
B) 0.1 km3 
C) 0.40 km3 
D) 0.20 km3 
E) 0.7 km3

Question 11

Use a change-of-base formula to evaluate   with a calculator or other technology. Round your answer to four decimal places. ​

Accepted Answer

A) 0.4582 
B) 2.6344 
C) 2.1827 
D) 3.4965 
E) 2.6391 
A) 0.4582 
B) 2.6344 
C) 2.1827 
D) 3.4965 
E) 2.6391

Question 12

Evaluate the logarithm by using properties of logarithms and the following fact. Round your answer two decimal places. ​   ​   ​

Accepted Answer

A) 10.40 
B) 1.91 
C) 4.60 
D) 6.76 
E) 5.20 
A) 10.40 
B) 1.91 
C) 4.60 
D) 6.76 
E) 5.20

Question 13

The president of a company predicts that sales N will increase after she assumes office and that the number of monthly sales will follow the curve given by   , where t represents time in months since she assumed office. What will be the sales after 9 months? Round your answer to the nearest month. ​

Accepted Answer

A) ​2,931 
B) ​1 
C) ​6 
D) ​1,620 
E) ​75 
A) ​2,931 
B) ​1 
C) ​6 
D) ​1,620 
E) ​75

Question 14

Solve the logarithmic equation   . ​

Accepted Answer

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

Question 15

Solve the logarithmic equation   . Round your answer to three decimal places. ​

Accepted Answer

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

Question 16

If $7,000 is invested at an annual rate of 11.5% compounded continuously, the future value S at any time t (in years) is given by   . What is the amount after 12 months? Round your answer to the nearest cent. ​

Accepted Answer

A) $27,824.31 
B) $7,848.82 
C) $17,838.71 
D) $7,853.11 
A) $27,824.31 
B) $7,848.82 
C) $17,838.71 
D) $7,853.11

Question 17

Given   . Graph   and   for   . ​

Accepted Answer

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

Question 18

Use properties of logarithms or a definition to simplify the expression. ​
If   , find   .
​

Accepted Answer

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

Question 19

Use a calculator to evaluate the expression. Round your answer to two decimal places. ​   ​

Accepted Answer

A) 403.43 
B) 16.31 
C) 130.39 
D) 1096.63 
E) 32.62 
A) 403.43 
B) 16.31 
C) 130.39 
D) 1096.63 
E) 32.62

Question 20

The population y of a certain country was 100,000 in 1990 and 149,182 in 2000. Assume the formula   applies to the growth of the country's population. Estimate the population of the country in 2005. Round your answer to the nearest human. ​

Accepted Answer

A) 122,140 
B) 271,828 
C) 182,212 
D) 81,873 
E) 54,881 
A) 122,140 
B) 271,828 
C) 182,212 
D) 81,873 
E) 54,881

If the total cost (in dollars) for x units of a product is given by , what is the total cost of producing 180 units? Round your answer to the nearest cent.

Write the expression as the sum or difference of two logarithmic functions containing no exponents.

Let . Use a graphing utility to graph the functions and where . Identify the graphs of and below.

Use properties of logarithms or a definition to simplify the expression. Check the result with a change-of-base formula and a calculator. Round your answer two decimal places.

Use the following information. Chemists use the pH (hydrogen potential) of a solution to measure its acidity or basicity. The pH is given by the formula , where is the concentration of hydrogen ions in moles per liter. What value of is associated with pH level 13?

Let . Using a graphing utility, graph for and . What effect does c have on the graphs?

Between the years 1960 and 2002, the percent of women in the work force is given by , where x is the number of years past 1950 (Source: U.S. Bureau of Labor Statistics). What does this model estimate to be the percent of women in the work force in 2019? Round your answer to two decimal places.

Evaluate the logarithm by using properties of logarithms and the following facts. Round your answer to two decimal places.

Pollution levels in Lake Erie have been modeled by the equation , where x is the volume of pollutants (in cubic kilometers) and t is the time (in years) (Adapted from R. H. Rainey, Science 155 (1967), 1242-1243). Find the initial pollution level; that is, find x when .

Use a change-of-base formula to evaluate with a calculator or other technology. Round your answer to four decimal places.

Evaluate the logarithm by using properties of logarithms and the following fact. Round your answer two decimal places.

The president of a company predicts that sales N will increase after she assumes office and that the number of monthly sales will follow the curve given by , where t represents time in months since she assumed office. What will be the sales after 9 months? Round your answer to the nearest month.

Solve the logarithmic equation .

Solve the logarithmic equation . Round your answer to three decimal places.

If $7,000 is invested at an annual rate of 11.5% compounded continuously, the future value S at any time t (in years) is given by . What is the amount after 12 months? Round your answer to the nearest cent.

Given . Graph and for .

Use properties of logarithms or a definition to simplify the expression. If , find .

Use a calculator to evaluate the expression. Round your answer to two decimal places.

The population y of a certain country was 100,000 in 1990 and 149,182 in 2000. Assume the formula applies to the growth of the country's population. Estimate the population of the country in 2005. Round your answer to the nearest human.

Algebraic Concepts

Linear Equations and Functions

Quadratic and Other Special Functions

Matrices

Inequalities and Linear Programming

Mathematics of Finance

Introduction to Probability

Further Topics in Probability; Data Description

Derivatives

Applications of Derivatives

Derivatives Continued

Indefinite Integrals

Definite Integrals: Techniques of Integration

Functions of Two or More Variables

Filters

Exam 6: Exponential and Logarithmic Functions

If the total cost (in dollars) for x units of a product is given by , what is the total cost of producing 180 units? Round your answer to the nearest cent. ​

Write the expression as the sum or difference of two logarithmic functions containing no exponents. ​ ​

Let . Use a graphing utility to graph the functions and where . Identify the graphs of and below. ​

Use properties of logarithms or a definition to simplify the expression. Check the result with a change-of-base formula and a calculator. Round your answer two decimal places. ​

Use the following information. Chemists use the pH (hydrogen potential) of a solution to measure its acidity or basicity. The pH is given by the formula , where is the concentration of hydrogen ions in moles per liter. What value of is associated with pH level 13? ​

Let . Using a graphing utility, graph for ​ and . What effect does c have on the graphs? ​

Between the years 1960 and 2002, the percent of women in the work force is given by , where x is the number of years past 1950 (Source: U.S. Bureau of Labor Statistics). What does this model estimate to be the percent of women in the work force in 2019? Round your answer to two decimal places. ​

Evaluate the logarithm by using properties of logarithms and the following facts. Round your answer to two decimal places. ​ ​ ​

Pollution levels in Lake Erie have been modeled by the equation , where x is the volume of pollutants (in cubic kilometers) and t is the time (in years) (Adapted from R. H. Rainey, Science 155 (1967), 1242-1243). Find the initial pollution level; that is, find x when . ​

Use a change-of-base formula to evaluate with a calculator or other technology. Round your answer to four decimal places. ​

Evaluate the logarithm by using properties of logarithms and the following fact. Round your answer two decimal places. ​ ​ ​

Solve the logarithmic equation . ​

Solve the logarithmic equation . Round your answer to three decimal places. ​

If $7,000 is invested at an annual rate of 11.5% compounded continuously, the future value S at any time t (in years) is given by . What is the amount after 12 months? Round your answer to the nearest cent. ​

Given . Graph and for . ​

Use properties of logarithms or a definition to simplify the expression. ​ If , find . ​

Use a calculator to evaluate the expression. Round your answer to two decimal places. ​ ​

The population y of a certain country was 100,000 in 1990 and 149,182 in 2000. Assume the formula applies to the growth of the country's population. Estimate the population of the country in 2005. Round your answer to the nearest human. ​

Algebraic Concepts

Linear Equations and Functions

Quadratic and Other Special Functions

Matrices

Inequalities and Linear Programming

Mathematics of Finance

Introduction to Probability

Further Topics in Probability; Data Description

Derivatives

Applications of Derivatives

Derivatives Continued

Indefinite Integrals

Definite Integrals: Techniques of Integration

Functions of Two or More Variables

Filters

If the total cost (in dollars) for x units of a product is given by , what is the total cost of producing 180 units? Round your answer to the nearest cent.

Write the expression as the sum or difference of two logarithmic functions containing no exponents.

Let . Use a graphing utility to graph the functions and where . Identify the graphs of and below.

Use properties of logarithms or a definition to simplify the expression. Check the result with a change-of-base formula and a calculator. Round your answer two decimal places.

Use the following information. Chemists use the pH (hydrogen potential) of a solution to measure its acidity or basicity. The pH is given by the formula , where is the concentration of hydrogen ions in moles per liter. What value of is associated with pH level 13?

Let . Using a graphing utility, graph for and . What effect does c have on the graphs?

Between the years 1960 and 2002, the percent of women in the work force is given by , where x is the number of years past 1950 (Source: U.S. Bureau of Labor Statistics). What does this model estimate to be the percent of women in the work force in 2019? Round your answer to two decimal places.

Evaluate the logarithm by using properties of logarithms and the following facts. Round your answer to two decimal places.

Pollution levels in Lake Erie have been modeled by the equation , where x is the volume of pollutants (in cubic kilometers) and t is the time (in years) (Adapted from R. H. Rainey, Science 155 (1967), 1242-1243). Find the initial pollution level; that is, find x when .

Use a change-of-base formula to evaluate with a calculator or other technology. Round your answer to four decimal places.

Evaluate the logarithm by using properties of logarithms and the following fact. Round your answer two decimal places.

Solve the logarithmic equation .

Solve the logarithmic equation . Round your answer to three decimal places.

If $7,000 is invested at an annual rate of 11.5% compounded continuously, the future value S at any time t (in years) is given by . What is the amount after 12 months? Round your answer to the nearest cent.

Given . Graph and for .

Use properties of logarithms or a definition to simplify the expression. If , find .

Use a calculator to evaluate the expression. Round your answer to two decimal places.

The population y of a certain country was 100,000 in 1990 and 149,182 in 2000. Assume the formula applies to the growth of the country's population. Estimate the population of the country in 2005. Round your answer to the nearest human.