Deck 8: Exponential and Logarithmic Expressions, Equations and Functions

Question 1

The pH of a solution is 9.4. Find the hydronium ion concentration in moles per liter. Use scientific notation and round the mantissa to the nearest tenth.

A)
B)
C)
D)
E) none of these

Answer 1

Question 2

The loudness of normal conversation is 62 decibels. Find the intensity of sound in watts per square meter. Round the mantissa to the nearest tenth.

A)
B)
C)
D)
E) none of these

Answer 2

Question 3

The original amount of methylacetate is and . Find the amount of methylacetate left after 45 minutes. Round to the nearest hundredth.

A)
B)
C)
D)
E) none of these

Answer 3

Question 4

A)
B)
C)
D)
E) None of these

Question 5

A)
B)
C)
D)
E) None of these

Question 6

A)
B)
C)
D)
E) None of these

Question 7

A)
B)
C)
D)
E) None of these

Question 8

If $5000 is invested at an annual interest rate of 7% compounded 365 times per year, find the time in years and months when the future value is $7500. Round up to the nearest month.

A) 5 years 10 months
B) 5 years 9 months
C) 5 years 8 months
D) 5 years 7 months
E) None of these

Question 9

The function is a model of the exponential population growth of house mice, where t is time in years, and y is the population of the mice. Predict the population of the mice after 8 months.

A) 9 mice
B) 32 mice
C) 8 mice
D) 64 mice
E) None of these

Question 10

$10,000 is invested at an annual interest rate of 7% for 5 years. Find the future value of the investment, rounded to the nearest hundredth, if the interest is compounded monthly.

A) $14,176.25
B) $14,176.26
C) $99,508.86
D) $99,508.87
E) None of these

Question 11

$34,000 is invested at an annual interest rate of 8% for 2 years. Find the future value of the investment, rounded to the nearest hundredth, if the interest is compounded continuously.

A) $40,999.37
B) $39,898.87
C) $40,998.81
D) $39,899.37
E) None of these

Question 12

The concentration of hydronium ions in a solution is . Find the pH of the solution. Round to the nearest tenth.

A) 7.5
B) 7.4
C) 7.3
D) 7.2
E) None of these

Question 13

The intensity of sound from a clap of thunder is . Find the loudness in decibels. Round to the nearest whole number.

A) 119 decibels
B) 118 decibels
C) 121 decibels
D) 120 decibels
E) None of these

Question 14

The intensity of sound from a swarm of bees is . Find the loudness in decibels. Round to the nearest whole number.

A) 75 decibels
B) 76 decibels
C) 73 decibels
D) 74 decibels
E) None of these

Question 15

Use the change of base formula to rewrite .

A)
B)
C)
D)
E) None of these

Question 16

is between which two numbers?

A) 1 and 2
B) 3 and 4
C) 2 and 3
D) 4 and 5
E) None of these

Question 17

is between which two numbers.

A) 1 and 2
B) 2 and 3
C) 4 and 5
D) 5 and 6
E) None of these

Question 18

Use the power rule to rewrite the expression as a product and simplify as much as possible.

-

A) 5x
B) 10x
C) 10
D) 0
E) None of these

Question 19

Use the power rule to rewrite the expression as a product and simplify as much as possible.

-

A)
B)
C)
D)
E) None of these

Question 20

Use the power rule to rewrite the expression as a product and simplify as much as possible.

-

A)
B)
C) 7
D)
E) None of these

Question 21

Rewrite the expression as a single logarithm and simplify as much as possible.

-

A)
B)
C)
D)
E) None of these

Question 22

Rewrite the expression as a single logarithm and simplify as much as possible.

-

A)
B)
C)
D)
E) None of these

Question 23

Rewrite the expression as a single logarithm and simplify.

-

A)
B)
C)
D)
E) None of these

Question 24

Rewrite the expression as a single logarithm and simplify.

-

A) 2
B)
C) 10
D)
E) None of these

Question 25

Rewrite the expression as a single logarithm and simplify.

-

A)
B)
C)
D)
E) None of these

Question 26

Rewrite the expression as a single logarithm.

-

A)
B)
C)
D)
E) None of these

Question 27

Rewrite the expression as a single logarithm.

-

A)
B)
C)
D)
E) None of these

Question 28

Rewrite the expression as a single logarithm.

-

A)
B)
C)
D)
E) None of these

Question 29

Rewrite the expression as the sum and/or difference of logarithms of a single variable with no exponents.

A)
B)
C)
D)
E) None of these

Question 30

Graph the function

A)
B)
C)
D)
E) None of these

Question 31

Graph the function

A)
B)
C)
D)
E) None of these

Question 32

Imagine graphing the four functions on the same coordinate system.
For which of these functions do the output values increase fastest?

A) I
B) II
C) III
D) IV
E) They increase at the same rate.

Question 33

Imagine graphing the four functions on the same coordinate system.
For which of these functions do the outputs decrease fastest?

A) I
B) IV
C) III
D) II
E) They decrease at the same rate.

Question 34

Use to find

A)
B)
C)
D)
E) None of these

Question 35

Use to find

A)
B)
C)
D)
E) None of these

Question 36

Use , to find

A)
B)
C)
D)
E) None of these

Question 37

Use and to find

A)
B)
C)
D)
E) None of these

Question 38

Use and to find

A)
B)
C)
D)
E) None of these

Question 39

Use and to represent the domain of by using interval notation.

A)
B)
C)
D)
E) None of these

Question 40

Find If And

A)
B)
C)
D)
E) None of these

Question 41

Use And To find

A)
B)
C)
D)
E) None of these

Question 42

Use And To represent the range of
by using interval notation.

A)
B)
C)
D)
E) None of these

Question 43

Use And To find

A)
B)
C)
D)
E) None of these

Question 44

Use And To represent the range of by using interval notation.

A)
B)
C)
D)
E) None of these

Question 45

Determine which of the following graphs, if any, represents a one-to-one function.
I
II
III

A) I only
B) II only
C) III only
D) I and III
E) None of these

Question 46

It costs a company $5.50 to produce a certain model of stop watch. The stop watch sells for $21.99 each. Write a profit function And use it to find the profit from selling 5,000 stop watches of this model. ( Where Is the revenue from selling Stop watches and Is the cost of producing stop watches.)

A) $82,450
B) $8,245
C) $8,245,000
D) $824,500
E) None of these

Question 47

If And , find

A)
B)
C)
D)
E) None of these

Question 48

The bookstore at a local college is having an end-of-term sale with all electronic tablets discounted 30%. The function Represents the relationship of the original price of the item, , and the price of the item on sale. The function Describes the cost of an item including sales tax. A student is buying a tablet with an original price of $800. Find

A)
B)
C)
D)

E) None of these