Question 1

Solve the problem.
-Ultraviolet solar radiation (UV) is strongly absorbed by ocean water. The intensity of the UV at a particular depth can be calculated using the equation  where d is the depth in centimeters  is the
Intensity at the surface, and I is the intensity at depth d. Find the depth at which the intensity is 20% of its value
At the surface. Round to the nearest tenth when necessary.

Accepted Answer

A)  16.1 cm 
B)  8.6 cm 
C)  5.4 cm 
D)  2.3 cm

Question 2

Write the equation of the graph in its final position.
-The graph of y = ln(x) is translated 2 units to the right, reflected in the x-axis, and then translated 7 units downward.

Accepted Answer

A)  y = ln(-x + 7) - 7 
B)  y = ln(x - 2) + 7 
C)  y = -ln(x - 2) - 7 
D)  y = ln(x + 2) + 7

Question 3

Use a graph or a table to find the limit.
-

Accepted Answer

A)  100 
B)   
C)  0 
D)

Question 4

Graph the function.
-

Accepted Answer

A)   
B)   
C)   
D)

Question 5

Solve the problem.
-If $2500 is invested in an account that pays interest compounded continuously, how long will it take to grow to $5000 at 5.5%? Round to the nearest tenth.

Accepted Answer

A)  3.8 years 
B)  12.6 years 
C)  11.5 years 
D)  13.2 years

Question 6

Simplify the expression.
-

Accepted Answer

A)  1 
B)  9 
C)   
D)  4x

Question 7

Use a calculator and the base-change formula to find the logarithm to four decimal places.
-

Accepted Answer

A)  1.2090 
B)  0.7893 
C)  1.7978 
D)  1.2670

Question 8

Solve the problem.
-At what interest rate must $4700 be compounded annually to equal $12,119.11 after 14 yr? (Round to the nearest percent.)

Accepted Answer

A)  9% 
B)  7% 
C)  8% 
D)  6%

Question 9

Find the value of the logarithmic function.
-

Accepted Answer

A)   
B)   
C)   
D)

Question 10

Rewrite the expression as a single logarithm.
-

Accepted Answer

A)   
B)   
C)   
D)

Question 11

Fill in the missing coordinate in each ordered pair so that the pair is a solution to the given equation.
-

Accepted Answer

A)   
B)   
C)   
D)

Question 12

Solve the problem.
-Coffee is best enjoyed at a temperature of 115°F. A restaurant owner wants to discover the temperature T at which he should serve his coffee so that it will have cooled to this ideal temperature in 6 minutes. He discovers
That a cup of coffee served at 197°F cools to 185°F in one minute when his restaurant is at 75°F. If he maintains
The restaurant temperature at 75°F, at what temperature should he serve the coffee to meet his goal?

Accepted Answer

A)  149°F 
B)  169°F 
C)  197°F 
D)  144°F

Question 13

Solve the equation.
-

Accepted Answer

A)   
B)  81 
C)   
D)  64

Question 14

Solve the equation.
-

Accepted Answer

A)  9 
B)  5 
C)  8 
D)  6

Question 15

Write the equation of the graph in its final position.
-The graph of y =  is translated 9 units to the right, reflected in the y-axis, and then translated 4 units downward.

Accepted Answer

A)   
B)   
C)   
D)

Question 16

Rewrite the expression as a sum or difference of logarithms or multiples of logarithms.
-

Accepted Answer

A)   
B)   
C)   
D)

Question 17

Rewrite the expression in terms of log(2) and log(5).
-

Accepted Answer

A)  log(-10) 
B)   
C)  5 log(-2) 
D)  -2 log(5)

Question 18

Use a graphing calculator to solve the equation. Round to two decimal places.
-

Accepted Answer

A)  -0.39 
B)  2.58 
C)  -2.58 
D)  -5.67

Question 19

Solve the problem. When needed, use 365 days per year and 30 days per month.
-An initial investment of $12,000 is appreciated for 5 years in an account that earns 4% interest, compounded quarterly. Find the amount of money in the account at the end of the period.

Accepted Answer

A)  $14,599.83 
B)  $2642.28 
C)  $14,642.28 
D)  $14,497.31

Question 20

Solve the problem.
-A certain noise produces  of power, designated as S. What is the decibel level of this noise?  Round to the nearest decibel.)

Accepted Answer

A)  69 decibels 
B)  8 decibels 
C)  182 decibels 
D)  79 decibels

Exam 4: Exponential and Logarithmic Functions

Write the equation of the graph in its final position. -The graph of y = ln(x) is translated 2 units to the right, reflected in the x-axis, and then translated 7 units downward.

Use a graph or a table to find the limit. -

Graph the function. -

Solve the problem. -If $2500 is invested in an account that pays interest compounded continuously, how long will it take to grow to $5000 at 5.5%? Round to the nearest tenth.

Simplify the expression. -

Use a calculator and the base-change formula to find the logarithm to four decimal places. -

Solve the problem. -At what interest rate must $4700 be compounded annually to equal $12,119.11 after 14 yr? (Round to the nearest percent.)

Find the value of the logarithmic function. -

Rewrite the expression as a single logarithm. -

Fill in the missing coordinate in each ordered pair so that the pair is a solution to the given equation. -

Solve the equation. -

Solve the equation. -

Write the equation of the graph in its final position. -The graph of y = is translated 9 units to the right, reflected in the y-axis, and then translated 4 units downward.

Rewrite the expression as a sum or difference of logarithms or multiples of logarithms. -

Rewrite the expression in terms of log(2) and log(5) . -

Use a graphing calculator to solve the equation. Round to two decimal places. -

Solve the problem. When needed, use 365 days per year and 30 days per month. -An initial investment of $12,000 is appreciated for 5 years in an account that earns 4% interest, compounded quarterly. Find the amount of money in the account at the end of the period.

Solve the problem. -A certain noise produces of power, designated as S. What is the decibel level of this noise? Round to the nearest decibel.)