Question 1

Solve the equation without using a calculator.

Accepted Answer

A) 1 and 10 
B) 2 and 1,000,000 
C) 1,000,000 
D) 1 and 10,000,000 
E) 10,000,000

Question 2

If $900 is deposited in a savings account that pays interest at a rate of  % per year compounded continuously, find the balance after 7 years.

Accepted Answer

A) $1,418.56 
B) $581.08 
C) $1,369.77 
D) $1,393.95 
E) $3,484.87

Question 3

Sketch the graph of the function.

Accepted Answer

A)   
B)   
C)   
D)

Question 4

The air pressure p (h) (in lb/ in 2 ) at an altitude of h feet above sea level may be approximated by the formula  At approximately what altitude h is the air pressure 9 lb/ in 2  ?

Accepted Answer

A) 12,743 ft 
B) 1,274 ft 
C) 17,123 ft 
D) 5,534 ft 
E) 553 ft

Question 5

How much money, invested at an interest rate of 10% per year compounded continuously, will amount to $98,000 after 16 years?

Accepted Answer

A) $19,785.86 
B) $97,982.32 
C) $39,571.72 
D) $4,853.97 
E) $108,306.75

Question 6

Find the inverse function of  .

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 7

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

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 8

Find an exponential function of the form f (x) = ba x  that has the given y-intercept and passes through the point P: y-intercept = 125; P (3,1);

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 9

Ventilation is an effective way to improve indoor air quality. In nonsmoking restaurants, air circulation requirements (in  ) are given by the function  , where x is the number of people in the dining area. Find  . Use  to determine the maximum number of people that should be in a restaurant having a ventilation capability of 2,700  .

Accepted Answer

A) 72 
B) 73 
C) 77 
D) 79 
E) 78

Question 10

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

Accepted Answer

A) 4log  7  ( x ) + log  7  ( w ) - 3log  7  ( y ) - 2log  7  ( z ) 
B) 4log  7  ( x ) + log  7  ( w ) + 2log  7  ( y ) + 3log  7  ( z ) 
C) log  7  ( x ) + log  7  ( w ) - log  7  ( y ) + log  7  ( z ) 
D) 4log  7  ( x ) + log  7  ( w ) - 2log  7  ( y ) - 3log  7  ( z ) 
E) 4log  7  ( x ) - log  7  ( w ) + 2log  7  ( y ) - 3log  7  ( z )

Question 11

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 1.7 volts to 4 volts.

Accepted Answer

A) db = 17.1 
B) db = 6.3 
C) db = 11.2 
D) db = 7.4 
E) db = 9.7

Question 12

Change to logarithmic form.

Accepted Answer

A) ln 100,000 = 6 
B) ln 100,000 = 5 
C) log 5 = 500,000 
D) log 100,000 = 5 
E) log 100,000 = 6

Question 13

The graph of a one-to-one function f is shown. Use the reflection property to sketch the graph of

Accepted Answer

A)   
B)   
C)   
D)

Question 14

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

Accepted Answer

A) log  9  ( x ) + log  9  ( w ) - log  9  ( y ) + log  9  ( z ) 
B) 3log  9  ( x ) + log  9  ( w ) + 5log  9  ( y ) + 2log  9  ( z ) 
C) 3log  9  ( x ) + log  9  ( w ) - 5log  9  ( y ) - 2log  9  ( z ) 
D) 3log  9  ( x ) - log  9  ( w ) + 5log  9  ( y ) - 2log  9  ( z ) 
E) 3log  9  ( x ) + log  9  ( w ) - 2log  9  ( y ) - 5log  9  ( z )

Question 15

In fishery science, a cohort is the collection of fish that results from one annual reproduction. It is usually assumed that the number of fish N( t ) still alive after t years is given by an exponential function. For Pacific halibut,  , where N o  is the initial size of the cohort. Approximate the percentage of the original number still alive after 14 years.

Accepted Answer

A) 6.1% 
B) 28.0% 
C) 2.0% 
D) 12.2% 
E) 81.8%

Question 16

Find an exponential function of the form f (x) = ba x  that has the given y-intercept and passes through the point P: y-intercept = 125; P (3,1);

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 17

Solve the equation:

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 18

Sketch the graph of

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 19

Solve the equation:

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 20

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

Accepted Answer

A)   
B)   
C)   
D)   
E)

Exam 5: Inverse, Exponential, and Logarithmic Functions

Solve the equation without using a calculator.

If $900 is deposited in a savings account that pays interest at a rate of % per year compounded continuously, find the balance after 7 years.

Sketch the graph of the function.

The air pressure p (h) (in lb/ in²) at an altitude of h feet above sea level may be approximated by the formula At approximately what altitude h is the air pressure 9 lb/ in² ?

How much money, invested at an interest rate of 10% per year compounded continuously, will amount to $98,000 after 16 years?

Find the inverse function of .

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

Find an exponential function of the form f (x) = ba^x that has the given y-intercept and passes through the point P: y-intercept = 125; P (3,1) ;

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

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 1.7 volts to 4 volts.

Change to logarithmic form.

The graph of a one-to-one function f is shown. Use the reflection property to sketch the graph of

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

Find an exponential function of the form f (x) = ba^x that has the given y-intercept and passes through the point P: y-intercept = 125; P (3,1) ;

Solve the equation:

Sketch the graph of

Solve the equation:

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

Exam 5: Inverse, Exponential, and Logarithmic Functions

Solve the equation without using a calculator.

If $900 is deposited in a savings account that pays interest at a rate of % per year compounded continuously, find the balance after 7 years.

Sketch the graph of the function.

The air pressure p (h) (in lb/ in 2 ) at an altitude of h feet above sea level may be approximated by the formula At approximately what altitude h is the air pressure 9 lb/ in 2 ?

How much money, invested at an interest rate of 10% per year compounded continuously, will amount to $98,000 after 16 years?

Find the inverse function of .

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

Find an exponential function of the form f (x) = ba x that has the given y-intercept and passes through the point P: y-intercept = 125; P (3,1) ;

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

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 1.7 volts to 4 volts.

Change to logarithmic form.

The graph of a one-to-one function f is shown. Use the reflection property to sketch the graph of

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

Find an exponential function of the form f (x) = ba x that has the given y-intercept and passes through the point P: y-intercept = 125; P (3,1) ;

Solve the equation:

Sketch the graph of

Solve the equation:

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

The air pressure p (h) (in lb/ in²) at an altitude of h feet above sea level may be approximated by the formula At approximately what altitude h is the air pressure 9 lb/ in² ?

Find an exponential function of the form f (x) = ba^x that has the given y-intercept and passes through the point P: y-intercept = 125; P (3,1) ;

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 1.7 volts to 4 volts.

Find an exponential function of the form f (x) = ba^x that has the given y-intercept and passes through the point P: y-intercept = 125; P (3,1) ;