Deck 4: Inverse, Exponential, and Logarithmic Functions

Question 1

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

A)
B)
C)
D)

Answer 1

C

Question 2

In 1980, the population of blue whales in the southern hemisphere was thought to number 5,000. The population N(t) has been decreasing according to the formula where t is in years and t = 0 corresponds to 1980. Predict the population in the year 2010 if this trend continues.

A)
B)
C)
D)
E)

Answer 2

C

Question 3

Find the inverse function of $f$ . $f ( x ) = 3 x + 6$

A) $f ^ { - 1 } ( x ) = \frac { ( x + 6 ) } { 3 }$
B) $f ^ { - 1 } ( x ) = \frac { ( x - 6 ) } { 3 }$
C) $f ^ { - 1 } ( x ) = \frac { 3 } { ( x - 6 ) }$
D) $f ^ { - 1 } ( x ) = \frac { 1 } { 3 } x - 6$
E) $f ^ { - 1 } ( x ) = \frac { 3 } { ( x + 6 ) }$

Answer 3

$f ^ { - 1 } ( x ) = \frac { ( x - 6 ) } { 3 }$

Question 4

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 25 days?

A) 3.125 milligrams
B) 12.125 milligrams
C) 5.125 milligrams
D) 8.125 milligrams
E) 2.125 milligrams

Question 5

Write the expression as one logarithm.

A)
B)
C)
D)
E)

Question 6

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);

A)
B)
C)
D)
E)

Question 7

Solve the equation.

A)
B)
C)
D)
E)

Question 8

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 ?

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

Question 9

Solve the equation:

A)
B)
C)
D)
E)

Question 10

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 3 volts.

A) db = 4.9
B) db = 8.7
C) db = 7.2
D) db = 11.4
E) db = 3.8

Question 11

Change to logarithmic form.

A) log 100 = 3
B) ln 100 = 2
C) ln 100 = 3
D) log 100 = 2
E) log 2 = 200

Question 12

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

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 13

Sketch the graph of

A)
B)
C)
D)
E)

Question 14

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.

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

Question 15

How much money, invested at an interest rate of 11% per year compounded continuously, will amount to $105,000 after 15 years?

A) $20,165.24
B) $117,209.20
C) $5,467.33
D) $40,330.48
E) $104,983.26

Question 16

The graph of a one-to-one function f is shown. Find the domain D and range R of the inverse function .

A)
B)
C)
D)
E)

Question 17

Some lending institutions calculate the monthly payment M on a loan of L dollars at an interest rate r (expressed as a decimal) by using the formula: where k = [1 + ( r / 12 )] ^12t and t is the number of years that the loan is in effect. An automobile dealer offers customers no-down-payment 8-year loans at an interest rate of 10%. If a customer can afford to pay $122 per month, find the price of the most expensive car that can be purchased.

A) $ 8,050.00
B) $ 8,045.62
C) $ 8,039.98
D) $ 8,048.79
E) $ 8,029.63

Question 18

Write the expression as one logarithm. 9ln ( x ) - 7ln - 4ln ( xy )

A) ln ( x ⁹ - y ⁷ - ( xy ) ⁴ )
B) ln ( 9x - 7y - 4xy )
C) ln ( x ³ y ⁵ )
D) ln ( x ⁵ y ³ )

Question 19

Sketch the graph of

A)
B)
C)
D)
E)

Question 20

Use the theorem on inverse functions to determine whether f and g are inverse functions of each other. $f ( x ) = 6 x - 1 ; g ( x ) = \frac { x + 1 } { 6 }$

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

Question 21

Solve the equation without using a calculator.

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 22

Find the solution of the equation.

A)
B)
C)
D)
E)

Question 23

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

A)
B)
C)
D)
E)

Question 24

An economist suspects that the points $( 0,6 ) , ( 1,3.152 ) , ( 2,1.656 ) , ( 3,0.870 )$ lie on the graph of $y = c 5 ^ { k x }$ , where $c$ and k are constants. If the data points have three-decimal-place accuracy, is this suspicion correct?

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