Question 1

Solve the equation.

Accepted Answer

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

Question 2

When the volume control on a stereo system is increased, the voltage across a loudspeaker changes from V 1  to V 2 , and the decibel increase is given by   Find the decibel increase if the voltage changes from 1.6 volts to 3.9 volts.

Accepted Answer

A) db = 13.0 
B) db = 11.6 
C) db = 21.4 
D) db = 9.3 
E) db = 8.2 
A) db = 13.0 
B) db = 11.6 
C) db = 21.4 
D) db = 9.3 
E) db = 8.2

Question 3

Solve the equation.

Accepted Answer

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

Question 4

Solve the equation.

Accepted Answer

A) 1 
B) 7 
C) 2 
D) 5 
E) 4 
A) 1 
B) 7 
C) 2 
D) 5 
E) 4

Question 5

An economist suspects that the points   lie on the graph of   , where   and   are constants. If the data points have three-decimal-place accuracy, is this suspicion correct?

Accepted Answer

A) The suspicion is incorrect 
B) The suspicion is correct 
A) The suspicion is incorrect 
B) The suspicion is correct

Question 6

An urban density model is a formula that relates the population density D ( in thousands/ mi 2  ) to the distance x (in miles) from the center of the city. The formula   for the central density a and coefficient of decay b has been found to be appropriate for many large U.S. cities. For the city of Atlanta in 1970, a = 5.5 and b = 0.10. At approximately what distance was the population density 800 per square mile?

Accepted Answer

A) 39.8 mi 
B) 19.3 mi 
C) 21.6 mi 
D) 8.4 mi 
E) 49.8 mi 
A) 39.8 mi 
B) 19.3 mi 
C) 21.6 mi 
D) 8.4 mi 
E) 49.8 mi

Question 7

Solve the equation:

Accepted Answer

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

Question 8

Use common logarithms to solve for x in terms of y.

Accepted Answer

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

Question 9

If monthly payments p are deposited in a savings account paying an annual interest rate r, then the amount A in the account after n years is given by:   Estimate n for p = 96, r = 0.04 and A = $177,664.

Accepted Answer

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

Question 10

Use the theorem on inverse functions to determine whether f and g are inverse functions of each other.

Accepted Answer

A) f and g are not inverse functions of each other. 
B) f and g are inverse functions of each other. 
A) f and g are not inverse functions of each other. 
B) f and g are inverse functions of each other.

Question 11

Simplify the expression.

Accepted Answer

A) 1 
B)    
C)    
D)    
E)    
A) 1 
B)    
C)    
D)    
E)

Question 12

Express in terms of logarithms of x, y, z, or w.

Accepted Answer

A) 3log  7  ( x ) + log  7  ( w ) + 5log  7  ( y ) + 4log  7  ( z ) 
B) log  7  ( x ) + log  7  ( w ) - log  7  ( y ) + log  7  ( z ) 
C) 3log  7  ( x ) + log  7  ( w ) - 4log  7  ( y ) - 5log  7  ( z ) 
D) 3log  7  ( x ) - log  7  ( w ) + 5log  7  ( y ) - 4log  7  ( z ) 
E) 3log  7  ( x ) + log  7  ( w ) - 5log  7  ( y ) - 4log  7  ( z ) 
A) 3log  7  ( x ) + log  7  ( w ) + 5log  7  ( y ) + 4log  7  ( z ) 
B) log  7  ( x ) + log  7  ( w ) - log  7  ( y ) + log  7  ( z ) 
C) 3log  7  ( x ) + log  7  ( w ) - 4log  7  ( y ) - 5log  7  ( z ) 
D) 3log  7  ( x ) - log  7  ( w ) + 5log  7  ( y ) - 4log  7  ( z ) 
E) 3log  7  ( x ) + log  7  ( w ) - 5log  7  ( y ) - 4log  7  ( z )

Question 13

If 7 grams of salt is added to a quantity of water, then the amount that is undissolved after t minutes is given by:   Sketch a graph that shows the value at any time from t = 0 to t = 10.

Accepted Answer

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

Question 14

The radioactive bismuth isotope  210 Bi has a half-life of 5 days. If there is 100 milligrams of 210 Bi present at t = 0, then the amount f(t) remaining after t days is given by:   How much 210 Bi remains after 5 days?

Accepted Answer

A) 59 milligrams 
B) 50 milligrams 
C) 49 milligrams 
D) 55 milligrams 
E) 52 milligrams 
A) 59 milligrams 
B) 50 milligrams 
C) 49 milligrams 
D) 55 milligrams 
E) 52 milligrams

Question 15

Solve the equation:

Accepted Answer

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

Question 16

The radioactive bismuth isotope  210 Bi has a half-life of 5 days. If there is 100 milligrams of 210 Bi present at t = 0, then the amount f(t) remaining after t days is given by:   How much 210 Bi remains after 5 days?

Accepted Answer

A) 52 milligrams 
B) 55 milligrams 
C) 50 milligrams 
D) 49 milligrams 
E) 59 milligrams 
A) 52 milligrams 
B) 55 milligrams 
C) 50 milligrams 
D) 49 milligrams 
E) 59 milligrams

Question 17

The Gompertz function,   is sometimes used to describe the sales of a new product whose sales are initially large but then level off toward a maximum saturation level. Graph the line and the Gompertz function with:

Accepted Answer

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

Question 18

If monthly payments p are deposited in a savings account paying an annual interest rate r, then the amount A in the account after n years is given by:   Estimate n for p = 90, r = 0.08 and A = $259,153.

Accepted Answer

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

Question 19

The Gompertz function,   is sometimes used to describe the sales of a new product whose sales are initially large but then level off toward a maximum saturation level. Graph the line and the Gompertz function with:

Accepted Answer

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

Question 20

If the pollution of Lake Erie were stopped suddenly, it has been estimated that the level y of pollutants would decrease according to the formula y = y o e -0.3937t  , where t is the time in years and y o  is the pollutant level at which further pollution ceased. How many years would it take to clear 59% of the pollutants?

Accepted Answer

A) t = 0.58 years 
B) t = 1.34 years 
C) t = 2.02 years 
D) t = 0.98 years 
E) t = 2.26 years 
A) t = 0.58 years 
B) t = 1.34 years 
C) t = 2.02 years 
D) t = 0.98 years 
E) t = 2.26 years

Solve the equation.

When the volume control on a stereo system is increased, the voltage across a loudspeaker changes from V₁ to V₂, and the decibel increase is given by Find the decibel increase if the voltage changes from 1.6 volts to 3.9 volts.

Solve the equation.

Solve the equation.

An economist suspects that the points lie on the graph of , where and are constants. If the data points have three-decimal-place accuracy, is this suspicion correct?

Solve the equation:

Use common logarithms to solve for x in terms of y.

If monthly payments p are deposited in a savings account paying an annual interest rate r, then the amount A in the account after n years is given by: Estimate n for p = 96, r = 0.04 and A = $177,664.

Use the theorem on inverse functions to determine whether f and g are inverse functions of each other.

Simplify the expression.

Express in terms of logarithms of x, y, z, or w.

If 7 grams of salt is added to a quantity of water, then the amount that is undissolved after t minutes is given by: Sketch a graph that shows the value at any time from t = 0 to t = 10.

The radioactive bismuth isotope ²¹⁰Bi has a half-life of 5 days. If there is 100 milligrams of ²¹⁰Bi present at t = 0, then the amount f(t) remaining after t days is given by: How much ²¹⁰Bi remains after 5 days?

Solve the equation:

The radioactive bismuth isotope ²¹⁰Bi has a half-life of 5 days. If there is 100 milligrams of ²¹⁰Bi present at t = 0, then the amount f(t) remaining after t days is given by: How much ²¹⁰Bi remains after 5 days?

The Gompertz function, is sometimes used to describe the sales of a new product whose sales are initially large but then level off toward a maximum saturation level. Graph the line and the Gompertz function with:

If monthly payments p are deposited in a savings account paying an annual interest rate r, then the amount A in the account after n years is given by: Estimate n for p = 90, r = 0.08 and A = $259,153.

The Gompertz function, is sometimes used to describe the sales of a new product whose sales are initially large but then level off toward a maximum saturation level. Graph the line and the Gompertz function with:

Fundamental Concepts of Algebra

Equations and Inequalities

Functions and Graphs

Polynomial and Rational Functions

The Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometry

Systems of Equations and Inequalities

Sequences, Series and Probability

Topics From Analytic Geometry

Filters

Exam 5: Inverse, Exponential, and Logarithmic Functions

Solve the equation.

When the volume control on a stereo system is increased, the voltage across a loudspeaker changes from V 1 to V 2 , and the decibel increase is given by Find the decibel increase if the voltage changes from 1.6 volts to 3.9 volts.

Solve the equation.

Solve the equation.

An economist suspects that the points lie on the graph of , where and are constants. If the data points have three-decimal-place accuracy, is this suspicion correct?

Solve the equation:

Use common logarithms to solve for x in terms of y.

If monthly payments p are deposited in a savings account paying an annual interest rate r, then the amount A in the account after n years is given by: Estimate n for p = 96, r = 0.04 and A = $177,664.

Use the theorem on inverse functions to determine whether f and g are inverse functions of each other.

Simplify the expression.

Express in terms of logarithms of x, y, z, or w.

If 7 grams of salt is added to a quantity of water, then the amount that is undissolved after t minutes is given by: Sketch a graph that shows the value at any time from t = 0 to t = 10.

The radioactive bismuth isotope 210 Bi has a half-life of 5 days. If there is 100 milligrams of 210 Bi present at t = 0, then the amount f(t) remaining after t days is given by: How much 210 Bi remains after 5 days?

Solve the equation:

The radioactive bismuth isotope 210 Bi has a half-life of 5 days. If there is 100 milligrams of 210 Bi present at t = 0, then the amount f(t) remaining after t days is given by: How much 210 Bi remains after 5 days?

The Gompertz function, is sometimes used to describe the sales of a new product whose sales are initially large but then level off toward a maximum saturation level. Graph the line and the Gompertz function with:

If monthly payments p are deposited in a savings account paying an annual interest rate r, then the amount A in the account after n years is given by: Estimate n for p = 90, r = 0.08 and A = $259,153.

The Gompertz function, is sometimes used to describe the sales of a new product whose sales are initially large but then level off toward a maximum saturation level. Graph the line and the Gompertz function with:

Fundamental Concepts of Algebra

Equations and Inequalities

Functions and Graphs

Polynomial and Rational Functions

The Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometry

Systems of Equations and Inequalities

Sequences, Series and Probability

Topics From Analytic Geometry

Filters

When the volume control on a stereo system is increased, the voltage across a loudspeaker changes from V₁ to V₂, and the decibel increase is given by Find the decibel increase if the voltage changes from 1.6 volts to 3.9 volts.

The radioactive bismuth isotope ²¹⁰Bi has a half-life of 5 days. If there is 100 milligrams of ²¹⁰Bi present at t = 0, then the amount f(t) remaining after t days is given by: How much ²¹⁰Bi remains after 5 days?

The radioactive bismuth isotope ²¹⁰Bi has a half-life of 5 days. If there is 100 milligrams of ²¹⁰Bi present at t = 0, then the amount f(t) remaining after t days is given by: How much ²¹⁰Bi remains after 5 days?