Question 1

Find the balance if $20,000 is invested at an annual rate of 9% for 8 years, compounded continuously.

Accepted Answer

A)  $175,067.89
B)  $21,872.49
C)  $9735.05
D)  $34,400.00
E)  $41,088.66 E

Question 2

Use algebraic procedures to find the exact solution of the equation  .

Accepted Answer

A)   
B)   
C)   
D)   
E)    E

Question 3

Use the change-of-base formula to graph the logarithmic function below.

Accepted Answer

A)   
B)   
C)   
D)   
E)    B

Question 4

A model for how long our coal resources will last is given by  where r is the percent increase in consumption from current levels of use and T is the time (in years)before the resources are depleted. If our consumption of coal increases by 14% per year, in how many years will we deplete our coal resources?

Accepted Answer

A)  88 years
B)  14 years
C)  29 years
D)  67 years
E)  39 years

Question 5

The population of a mid-sized city is growing exponentially. The population of the city was 250,000 in the year 2000 and 273,400 in 2004. Find the exponential growth function that models the population growth of the city. Use  to represent the year 2000.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 6

How long will it take $20,000 to double if it is invested in a savings account that pays 5.5% annual interest compounded continuously? Round to the nearest year.

Accepted Answer

A)  19 years
B)  8 years
C)  11 years
D)  12 years
E)  13 years

Question 7

If we assume that air resistance is proportional to the square of the velocity, then the time t in seconds required for an object to reach a velocity v in feet per second is given by  . Determine the vertical asymptote for the graph of this function.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 8

Use composition of functions to determine whether  and  are inverses of one another.

Accepted Answer

A) True 
 B)False

Question 9

Write the logarithmic equation  in its exponential form.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 10

In a small city, which has a population of 53,000 people, the number of people  exposed to a rumor in t hours is given by the function  . Find the number of hours until  % of the population have heard the rumor. Round to the nearest hour.

Accepted Answer

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

Question 11

Find the inverse of  ,  .

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 12

The function  models the relationship between the dollar amount x spent on advertising a product and the number of units N that a company can sell. Find the number of units that will be sold with advertising expenditures of $  .

Accepted Answer

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

Question 13

Use algebraic procedures to find the exact solution of the equation

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 14

Evaluate the logarithm  without using a calculator.

Accepted Answer

A)  3
B)  -3
C)  -2
D)  2
E)  100

Question 15

Write the equation below in its logarithmic form. Assume  .

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 16

Use algebraic procedures to find the exact solution of the equation  .

Accepted Answer

A)   
B)  0, -8
C)  9
D)   
E)  1

Question 17

Evaluate the following logarithmic expression.

Accepted Answer

A)  6
B)  9
C)  5
D)  4
E)  1

Question 18

The following table shows the time T , in hours, before a scuba diver wearing a certain thickness wet suit reaches hypothermia (95° F )for various water temperatures F , in degrees Fahrenheit. Water Temperature, ° F Time T , hours. Find an exponential regression model for the data. Round the parameters to the nearest thousandth.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 19

Explain how to use the graph of  to produce the graph of  .

Accepted Answer

A)  Shift the graph of f horizontally 2 units to the right and then shift this graph vertically downward 8 units.
B)  Shift the graph of f horizontally 8 units to the right and then shift this graph vertically upward 2 units.
C)  Shift the graph of f horizontally 2 units to the right and then shift this graph vertically upward 8 units.
D)  Shift the graph of f horizontally 8 units to the left and then shift this graph vertically downward 2 units.
E)  Shift the graph of f horizontally 2 units to the left and then shift this graph vertically downward 8 units.

Question 20

The function  gives the annual interest rate r , as a percent, a bank will pay on its money market accounts, where t is the term (the time the money is invested)in months. What is the minimum number of complete months during which a person must invest to receive an interest rate of at least 2.3%?

Accepted Answer

A)  17 months
B)  10 months
C)  19 months
D)  16 months
E)  8 months

Exam 4: Exponential and Logarithmic Functions

Find the balance if $20,000 is invested at an annual rate of 9% for 8 years, compounded continuously.

Use algebraic procedures to find the exact solution of the equation .

Use the change-of-base formula to graph the logarithmic function below.

The population of a mid-sized city is growing exponentially. The population of the city was 250,000 in the year 2000 and 273,400 in 2004. Find the exponential growth function that models the population growth of the city. Use to represent the year 2000.

How long will it take $20,000 to double if it is invested in a savings account that pays 5.5% annual interest compounded continuously? Round to the nearest year.

If we assume that air resistance is proportional to the square of the velocity, then the time t in seconds required for an object to reach a velocity v in feet per second is given by . Determine the vertical asymptote for the graph of this function.

Use composition of functions to determine whether and are inverses of one another.

Write the logarithmic equation in its exponential form.

In a small city, which has a population of 53,000 people, the number of people exposed to a rumor in t hours is given by the function . Find the number of hours until % of the population have heard the rumor. Round to the nearest hour.

Find the inverse of , .

The function models the relationship between the dollar amount x spent on advertising a product and the number of units N that a company can sell. Find the number of units that will be sold with advertising expenditures of $ .

Use algebraic procedures to find the exact solution of the equation

Evaluate the logarithm without using a calculator.

Write the equation below in its logarithmic form. Assume .

Use algebraic procedures to find the exact solution of the equation .

Evaluate the following logarithmic expression.

Explain how to use the graph of to produce the graph of .

The function gives the annual interest rate r , as a percent, a bank will pay on its money market accounts, where t is the term (the time the money is invested) in months. What is the minimum number of complete months during which a person must invest to receive an interest rate of at least 2.3%?