Math 095 Final Exam Review (updated 10/28/11) This review is an attempt to provide a comprehensive review of our course concepts and problem types, but there is no guarantee the final will only include problems like in this review. This is a good starting point in your review for the final, but you should also study the textbook, your notes and homework. Module I – Sections 1.1, 1.6, 2.1, 2.2, 2.3 1. Consider the graph of the function f to the right. a) How can you tell the graph represents a function? b) What is the independent variable? c) What is the dependent variable? d) What is the value of (6)f ? ( 2)f  ? e) For what values of x is ( ) 2f x  ? f) What is the domain of the function? g) What is the range of the function? - 2 - 1 2 6 5 4 3 1 654321- 1- 2 x y 2. Do the tables represent functions? How do you know? a) b) 3. The graph at right represents a scattergram and a linear model for the number of companies on the NASDAQ1 stock market between 1990 and 1999, where n represents the number of companies t years after 1990. a) Using the linear model, in what year were there approximately 3500 companies? b) What is the n-intercept of the linear model and what does it mean? c) What is the t-intercept and what does it mean? d) From the linear model, what would you predict the number of companies to be in the year 1996? x 3 5 7 3 5 y 2 6 8 9 6 x 5 4 2 1 0 y 2 6 8 9 6 Years since 1990 0 2 4 6 108 12 1 2 3 4 N um b er o f co m p an ie s (t h o us an ds ) Number of Companies on the Nasdaq Stock Market between 1990 and 1999n t 5 Online MTH095 Final Review 2 KA 10/28/2011 4. Find a linear equation of the line that passes through the given pairs of points. a) (3, 5) and (7,1) b) (4, 6) and (2, 0) 5. The average consumption of sugar in the U.S. increased from 26 pounds per person in 1986 to 136 pounds per person in 2006. Let p be the average number of pounds consumed t years after 1980. Find an equation of a linear model that describes the data. 6. If 2( ) 2 4f x x  , find the following. a) ( 3)f  b) (0)f c) (5.2)f Module 2 – Sections 4.1, 4.2, 4.3, 4.4, 4.5 7. Simplify each of the following and write without negative exponents. a) 2 3 4 y          b) 2 36 1 4 x y x y   c)  252 25 xxx  d) 4 10 p 8. Simplify each expression using the laws of exponents. Write the answers with positive exponents. a)   2 43 35 3x x Online MTH095 Final Review 3 KA 10/28/2011 b) 3 44 5 x x c) 3 52 3 m t        d)   1 26 4m n 9. Let 1 ( ) (4) 2 xf x  a) What is the y-intercept of the graph of f ? b) Does f represent growth or decay? c) Find ( 2)f  d) Find (2)f e) Find x when ( ) 32f x  10. Find ...

1. Math 095 Final Exam Review (updated 10/28/11)
This review is an attempt to provide a comprehensive review of
our course concepts and problem types, but there
is no guarantee the final will only include problems like in this
review. This is a good starting point in your review
for the final, but you should also study the textbook, your notes
and homework.
Module I – Sections 1.1, 1.6, 2.1, 2.2, 2.3
1. Consider the graph of the function f to the right.
a) How can you tell the graph represents a
function?
b) What is the independent variable?
c) What is the dependent variable?
d) What is the value of
(6)f ?
e)

2. f) What is the domain of the function?
g) What is the range of the function?
- 2
- 1
2
6
5
4
3
1
654321- 1- 2
x
y
2. Do the tables represent functions? How do you know?
a) b)

3. 3. The graph at right represents a scattergram and a linear
model for the number of companies on the NASDAQ1 stock
market between 1990 and 1999, where n represents the number
of companies t years after 1990.
a) Using the linear model, in what year were there
approximately 3500 companies?
b) What is the n-intercept of the linear model and what
does it mean?
c) What is the t-intercept and what does it mean?
d) From the linear model, what would you predict the
number of companies to be in the year 1996?
x 3 5 7 3 5
y 2 6 8 9 6
x 5 4 2 1 0
y 2 6 8 9 6
Years since 1990
0 2 4 6 108 12
1

4. 2
3
4
N
um
b
er
o
f
co
m
p
an
ie
s
(t
h
o
us
an
ds
)
Number of Companies on the Nasdaq Stock Market

5. between 1990 and 1999n
t
5
Online MTH095 Final Review 2
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4. Find a linear equation of the line that passes through the
given pairs of points.
a) (3, 5) and (7,1)
5. The average consumption of sugar in the U.S. increased from
26 pounds per person in 1986 to 136 pounds per person
in 2006. Let p be the average number of pounds consumed t
years after 1980. Find an equation of a linear model that
describes the data.
b) (0)f
c) (5.2)f

6. Module 2 – Sections 4.1, 4.2, 4.3, 4.4, 4.5
7. Simplify each of the following and write without negative
exponents.
a)
2
3
4
y
b)
2 36
1 4
x y
x y

7. c)
d)
4
10
8. Simplify each expression using the laws of exponents. Write
the answers with positive exponents.
Online MTH095 Final Review 3
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b)
3
44
5
x

8. x
c)
3
52
3
m
t
1
26 4m n
9. Let
1
( ) (4)
2
a) What is the y-intercept of the graph of f ?

9. b) Does f represent growth or decay?
d) Find (2)f
curve that contains the given set of points. (0, 7) and (3, 2).
11. Sue invested $4000 in an account that pays 6% interest
compounded annually.
Let ( )f t represent the value of the account after t years.
a) Write an equation for f.
b) What is the account worth after 12 years?

10. Online MTH095 Final Review 4
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Module 3 – Sections 5.2, 5.3, 5.4, and 5.6
12. Find the value of each logarithm.
a) 6log (36)
b) 12ln( )e
13. Rewrite the log equations in exponential form.
14. Rewrite the exponential equations in log form.
15. Solve each of the equations. Round decimal answers to
three places.

11. 16. A population of 35 fruit flies triples every day. Let ( )f t
be the number of flies after t days.
a) Write an equation for the function, f, that models the fruit
fly population growth.
b) How many fruit flies are there after 5 days?
c) How long will it take for the fruit fly population to reach
25000? Round decimal answers to two places.
17. The population of Smalltown decreased from 1910 to 1960,
as shown in the table at the right.
Let ( )P t be the population of Smalltown t years after 1910.
a) Use exponential regression to find an equation for P. Round
decimal numbers to four
places.

12. Year
1910
1920
1930
1940
1950
1960
Population
36000
17000
10050
4500
2100
1100
Online MTH095 Final Review 5
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b) What is the coefficient a in your model and what does it
represent?
c) Use your function to predict the year the population reaches
150.
Module 4 – Sections 7.2, 7.3, 7.5, 7.7, and 7.8

13. a) Which does the graph have, a maximum or a minimum?
b) Calculate the coordinates of the vertex by hand and using
the Maximum/Minimum feature on a calculator.
c) What is the y-intercept of the graph?
d) What are the x-intercepts of the graph?
19. Simplify the radical expressions:
a) 18
b)
17
49
20. Solve each of the equations:

14. Online MTH095 Final Review 6
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21. A football player kicks a ball. The height of the ball, h(t)
in feet, t seconds after it is kicked, is given by the equation
a) What is the height of the ball after 3 seconds?
b) At what time/s is the ball 5 feet off the ground
c) How long does it take the ball to hit the ground? Round

15. decimal answers to three places.
22. The population of Iceland (in thousands) from 1950 to 2000
is given in the table at the right.
a) What kind of equation fits the data best, quadratic or
exponential?
b) Use quadratic regression to find a model for the data where
f(t) is the population t years
after 1950. Round decimal numbers to three places.
c) Predict the year that maximum population is reached.
d) To the nearest person, predict the maximum population.
e) In what years does model breakdown occur?
Module 5 – Sections 8.5, 10,1, and 10.2
23. Translate the sentence into an equation. Use k for your
constant of variation.
P varies inversely as the square of r.

16. 24. Write an equation, then find the requested value of the
variable.
a) If t varies directly as the square of p, and t = 36 when p =
3, find t when p = 4.
b) If M varies inversely as the square root of r, and M = 3
when r = 25, find M when r = 9.
Year
1950
1960
1970
1980
1990
2000
Population
(thousands)
130
176
215
245
264
275
Online MTH095 Final Review 7
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17. 25. Using na notation, find a formula of each sequence.
b. 20, 100, 500, 2500, 12500
26. Find the 29th term of the sequence: 42, 47, 52, 57, 62, ...
27. Find the term number n of the last term of the finite
sequence: 7, 11, 15, 19, 23, ... 407
28. Find the 66th term of the sequence. Write your answer in
scientific notation if necessary.
6, 18, 54, 162, 486,...

18. 29. 100, 663, 296 is a term of the sequence 6, 24, 96, 384,
1536, ...
Find the term number n of that term.
30. Find an equation of a function f such that (1), (2), (3), (4),
(5), ...f f f f f