Deck 3: Exponential, Logistic, and Logarithmic Functions

Question 1

The population of Powerville is 425,000 , and it is increasing at a rate of 4.2% each year. Predict the number of years until the population will be 750,000 . Round to two decimal places.

Answer 1

13.81 years

Question 2

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Answer 2

Question 3

Answer 3

Question 4

A casserole is removed from a oven, and it cools
to after 15 minutes in a room. How long
(from the time it is taken out of the oven) does it take
to cool to (Hint: Use Newton's Law of Cooling,

Question 5

Solve the logarithmic equation log (x+2)+log x=3 log 2 algebraically. Identify any extraneous solutions.

Question 6

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Question 7

Graph the logistic function
Show the viewing window dimensions.

Question 8

Find the interval(s) where the function is decreasing.

A)
B)
C)
D)
E)

Question 9

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Question 10

Solve the logarithmic equation
for x . Leave the answer in radical form.

Question 11

Which equation is equivalent to

A) ln y=ln 7+5 ln x
B) y=ln 7+5 ln x
C) y=7+5 ln x
D) ln y=7+5 ln x
E) ln y=ln 7-5 ln x

Question 12

How long will it take an investment of $750 at 8.75% APR compounded quarterly to grow a $1000?

Question 13

Determine the domain of the function

A)
B) (0,4)
C) (-4,0)
D)
E)

Question 14

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FORM A DATE
3 Chapter Test NAME
Directions: Show all work where appropriate. A graphing calculator may be necessary to answer
some questions.

Question 15

Question 16

A bank advertises that currently a CD pays 6 % APR compounded daily (use 365 days a year). What is the effective yield on this CD, to the nearest hundredth?

Question 17

Which expression is equivalent to ln

A)
B)
C)
D)
E)

Question 18

Write the exponential equation in logarithmic form.

Question 19

Solve graphically.

Question 20

List the transformations used to obtain the graph of from the graph of

Question 21

A pie is removed from a oven and cools to after 15 minutes in a room at How long (from the time it is removed from the oven) will it take the pie to cool to

Question 22

Solve the log (x-5)+log (x-2)=1 algebraically. List any extraneous solutions and explain. If there are no extraneous solutions, explain why not.

Question 23

What is the natural logarithmic regression equation for the following data? Estimate the y -value for x=15 . Express answers to the nearest hundredth.

Question 24

What is the natural logarithmic regression equation for
the following data? Estimate the y-value for x = 18.
Express answers to the nearest hundredth.

Question 25

Solve for

Question 26

Question 27

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FORM A

Question 28

Show that
are inverse functions.

Question 29

When Jose was born, his grandmother deposited $8,000 into an account paying 6% interest, compounded quarterly. How much money will be available to use for college tuition 18 years later?

Question 30

Graph the function

Question 31

Solve the equation 8 - 3 ln x = 12. Give an exact
answer as well as its decimal approximation (to the
nearest hundredth).

Question 32

A single-cell amoeba doubles every 3 days. How long
would it take one amoeba to produce a population of
about 10,000 amoebae?

Question 33

(a) Solve for
(b) Solve for

Question 34

To finance their new home, the Colemans have agreed to a $90,000 mortgage loan at 9.25% APR. What will their monthly payments be if the loan has a term of 15 years?

A)
B)
C)
D)
E)

Question 35

For the function
(a) Find the horizontal asymptotes.
(b) Find the domain and range.
(c) Describe the end behavior.

Question 36

Question 37

Graph the function

Question 38

Let
Solve for t .

A)
B)
C)
D)
E)

Question 39

(a) Solve for
(b) Solve for

Question 40

A single-cell amoeba doubles every 4 days. How long
would it take one amoeba to produce a population of
about 10,000 amoebae?

Question 41

Solve the equation 7-4 log x=10 . Give an exact answer as well as its decimal approximation (to the nearest hundredth).

Question 42

A certain company estimates that the computer they plan
to buy in 30 months will cost $5,250. How much money
should be deposited now into an account paying 6.25%
interest, compounded monthly so there will be enough
money to pay cash for the computer in 30 months?

Question 43

When Kara was born, her grandmother deposited
$10,500 into an account paying 6.4% interest,
compounded quarterly. How much money will be
available to use for college tuition 18 years later?

Question 44

For the function
(a) Find the horizontal asymptotes.
(b) Find the domain and range
(c) Describe the end behavior.

Question 45

Juan deposits $200 each month into a retirement
account that pays 9.00% APR (0.75% per month).
What is the value of this annuity after 30 years?

Question 46

Solve the equation log (x-4)+log (x+5)=1 algebraically. List any extraneous solutions and explain If there are no extraneous solutions, explain why not.

Question 47

Show that
are inverse functions.

Question 48

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Question 49

To finance their new home, the Tiballis have agreed to an $80,000 mortgage loan at 8.75% APR. What will their monthly payments be if the loan has a term of 20 years?

A)
B)
C)
D)
E)

Question 50

Solve for

Question 51

A casserole is removed from an oven at and cools to after 25 minutes in a room at How long (from the time it is removed from the oven) will it take the casserole to cool to

Question 52

Let Solve for t .

A)
B)
C) ln a+ln 1.06
D)
E)