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MAT 170-Precalculus
Instructor: Dawn Teuscher
Exam 2
Fall 2009
Module 3 and 4
Exam 2
Student Name (Print)
Date
Test Instructions
a. You must show your work on this exam wherever possible. Please read each problem carefully,
and provide complete and well-organized answers.
b. Answers without supporting work will be given zero credit. Partial credit is granted only if work
is shown.
c. No calculators with Qwerty keyboards or ones like the Casio FX-2, TI-89 or TI-92 that do
symbolic algebra may be used.
d. Proctors reserve the right to check calculators.
e. The usage of cell phones is prohibited. TURN YOUR CELL PHONE OFF! Do not allow your
cell phone to ring while you are taking the exam. Do not use the calculator on your cell phone. If
a proctor sees you using a cell phone, they will take your exam away from you.
© 2008 Carlson and Oehrtman
Page 1 of 7
MAT 170-Precalculus
Instructor: Dawn Teuscher
Exam 2
Fall 2009
Use the following table to complete items 1 and 2 (2 pts. for each)
1) Determine g 1 (1) .
a. -1
b. 0
c. 1
d. 2
e. 3
2) Determine f g 3.
a. 4
b. -1
c. 0
d. 1
e. 5
x
-2
-1
0
1
2
3
f (x ) g (x )
0
3
4
-1
6
-2
5
3
2
1
-1
0
3) (16 pts.) The number of H1N1 flu sufferers at Arizona State University was report to be 72 on
October 28th. The prediction was that the number of H1N1 cases would grow to 438 on
December 9th (6 weeks after October 28th). Let N represent the number of H1N1 flu cases at
ASU t weeks after October 28th. Hint: Let (0, 72) be one point
a. Express N as a linear function of t. Explain the slope and y-intercept in the context of
the problem.
b. Express N as an exponential function of t. Explain the growth factor and the yintercept in the context of the problem.
© 2008 Carlson and Oehrtman
Page 2 of 7
MAT 170-Precalculus
Instructor: Dawn Teuscher
4)
Exam 2
Fall 2009
(12 pts.) Use the graph of f to determine the
following:
a.
f 1 3 
b.
f (2) 
c.
f 1 5  =
d.
f (5)  f (3) =
e.
2 f 4   f 2  
5) (3 pts.) An oil spill has a circular boundary that is growing outward from the center of the
spill at a speed of 2 feet per second. Express the area, A, of the circular spill in terms of the
number of seconds, n, that have passed since the oil was spilled.

a. A  4 n
b. Ar2
c. A  4 n2
d. A  2 n2
e. A
n2
6) (3 pts.) Use the graphs of f and g to the right to evaluate f(g(2))

a.
b.
c.
d.
e.
-2
1
0
2
3
y
g
(4,3)
(-2,1)
f
x
(2,-2)
© 2008 Carlson and Oehrtman
Page 3 of 7
MAT 170-Precalculus
Instructor: Dawn Teuscher
Exam 2
Fall 2009
7) (20 pts.) Suppose that the mass (in grams) of a sample of radioactive material decays at a
continuous rate of 0.20% per year. The initial mass of the radioactive material is 120 grams.
a. Write a function, f, that gives the mass of radioactive materials remaining, m, as a
function of time, t, in years.
b. How long will it take to have 100 grams of radioactive material remaining? Show your
work.
c. Rewrite this function in the form 𝑚 = 𝑓 𝑡� = 𝑎 𝑏�𝑡�.
d. By what rate (keep at least 4 decimal places) is the radioactive material decaying
every year?
2
8) (2 pts.) Given the function f, defined by f(x) = 3x + 2x – 4, find f(x + a).
a.
b.
c.
d.
e.
f(x + a) = 3x2 + 3a2 + 2x + 2a – 4
f(x + a) = 3x2 + 6xa + 3a2 + 2x – 4
f(x + a) = 3 (x + a)2 + 2(x + a) – 4
f(x + a) = 3 (x + a)2 + 2x – 4
f(x + a) = 3x2 + 2x – 4 + a
© 2008 Carlson and Oehrtman
Page 4 of 7
MAT 170-Precalculus
Instructor: Dawn Teuscher
Exam 2
Fall 2009
9) (2 pts.) The model that describes the number of bacteria in a culture after t days has just been
t
t
updated from P(t)  7(2) to P(t)  7(3) . What implications can you draw from this
information?
a. The final number of bacteria is 3 times as much of the initial value instead of 2 times
as much.
b. The initial number of bacteria is 3 instead of 2.
c. The number of bacteria triples every day instead of doubling every day.
d. The growth rate of the bacteria in the culture is 30% per day instead of 20% per day.
e. None of the above.
10) (15 pts.) Vanessa invested $22,100 in an account that pays 6.5% interest per year
compounded monthly.
a. Write a formula to determine the amount of money, A, in Vanessa’s account after t
years.
b. What is the effective interest rate—that is, what actual interest rate does Vanessa
receive per year on her money?
c. How much money is in Vanessa’s account after 12 years, assuming no additional
deposits or withdrawals are made after the initial investment?
d. Vanessa decided to close out her account to make a down payment on a house. When
she closed out her account she received $28,542. How many years had passed since
Vanessa initially invested her money? (Round your answer to the nearest tenth.)
© 2008 Carlson and Oehrtman
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MAT 170-Precalculus
Instructor: Dawn Teuscher
Exam 2
Fall 2009
11) (8 pts.) Determine the inverse of the following functions and state if the inverse is a function.
i. f (x)  7x  5
ii. g(x)  x 2  3
12) (14 pts.) Use the following tables to determine:
a. whether the following data represents a linear or exponential function and explain
your reasoning.
b. an equation relating the two variables for each of table.
i.
X
-2
0
2
4
6
8
Y
-7
-3
1
5
9
13
ii.
X
-3
0
3
6
9
12
Y
7.0925
5
3.5248
2.4849
1.7518
1.235
© 2008 Carlson and Oehrtman
Page 6 of 7
MAT 170-Precalculus
Instructor: Dawn Teuscher
© 2008 Carlson and Oehrtman
Exam 2
Fall 2009
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