MAT 152 Final Exam 100% Correct
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Common Final Exam,
SP2015
Name: _______________
Show all necessary work! Answers
without work may not receive any partial credit.
Round all decimal answers to one
decimal place unless otherwise
instructed.
1.
Solve the following equations. There
is one of each type we studied this semester. Show all
necessary work.
a.
2
(
6
)
푥
=
1296
b.
푥
2
−
6
푥
<
7
c.
3
푥
3
−
4
푥
2
−
12
푥
+
16
=
0
d.
|
푥
−
1
2
|
=
3
e.
√
3
푥
2
+
4
−
2
푥
=
0
f.
푙표푔
4
64
=
푥
g
.
푙표푔
2
푥
+
푙표푔
2
(
푥
−
6
)
=
4
Page
2
of
7
Applications!!
J
2.
A company has determined that its
profit for a product can be described by a linear
function.
The profit from the production and
sale of 150 units is $455 and the profit from 250
units is $895.
- Find
the rate of change of profit for
this product when between 150 and 250 units are sold.
- Write the equation of the profit function for this product
here.
c.
Use the profit function equation to
predict the profit from the
Sale of 280
units.
d.
How many units have to be sold for
the break
–
even point for this product?
3.
Solve the system of equations using
a matrix.
{
2
푥
+
4
푦
−
14
푧
=
0
3
푥
+
5
푦
+
푧
=
19
푥
+
4
푦
−
푧
=
12
a
c
b
d
Page
3
of
7
4.
A ball is thrown upward at 96 feet
per second from the top of a
building that is 100 feet high.
The
height of the ball can be modeled by
푆
=
100
+
96
푡
−
16
푡
2
feet where t is the number of
seconds
after the ball is thrown.
a.
When will the ball reach a height of
230 feet?
b.
When will
the ball reach the ground?
c.
When will th
e ball reach its maximum height?
d.
What is the ball’s maximum height?
5.
A class of
initially
physically
–
fit college algebra students
neglected their exercise over the course
of the semester and consented to
weekly physical
–
fitness tests during this time. The
fitness test
average “fitness rating”,
퐹
(
푡
)
,
is between 1 and 10, with 10 being
as physi
cally fit as Tarzan and
1 being an utter and complete Mr.
Couch Potato.
푡
represents the number of weeks from
the
beginning of the semester. This
scenario is modeled by the function
퐹
(
푡
)
=
10
−
7
.
3
푙표푔
(
푡
+
1
)
;
0
≤
푡
≤
16
a.
What was the average fitness rati
ng when the
physical
–
fitness test was first administered?
b.
What was the average rating at the
end of the 16
–
week semester?
c.
During which week was
the average fitness rating
3
?
a
b
c
a
b
d
c
Page
4
of
7
6.
Below is a piecewise
–
defined function T with input x that
models the tax dollars owed as a
function of x, the income, with
0
<
푥
≤
104
,
630
.
푇
(
푥
)
=
{
0
.
13
푥
푖푓
0
<
푥
≤
39
,
600
5
,
148
.
00
+
0
.
21
(
푥
−
39
,
600
)
푖푓
39
,
600
<
푥
≤
104
,
630
- Use the function to find
푇
(
25
,
000
)
.
b.
Find the tax owed on an income of
$53,000.
c.
A friend tells you not to earn any
money over $39,000 because it would raise your tax rate to
21% on all of your income. Test this
statement by
finding the tax
on $39,600 and on $39,610.
d.
Does earning $39,610 raise your
income tax rate to 21% on all of
your income?
7.
Given the function
푅
(
푥
)
=
18
푥
−
3
, find the inverse of
푅
(
푥
)
.
a
b
c
d
Page
5
of
7
8.
The table at right gives the
average
of total property crimes as the
number per 1000 households
for each of the years 1980
–
2001.
Round decimals to 2 places.
a.
Find a cubic model that is the best
fit for this data,
with x equal to the number of years
after 1980.
Record the
rounded
model here:
b.
Find a quartic model that is the
best fit for this data,
with x equal to the number of years
after 1980.
Record the
r
ounded
model here:
c.
Which model
is the
better fit for the data? Explain
your choice.
d.
What does the
better
model predict the
average
total property crime to be for 2011
(use the rounded
model)
?
Year
Total
Property
Crime
Year
Total
Property
Crime
1980
496.1
1991
353.7
1981
497.2
1992
325.3
1982
468.3
1993
318.9
1983
428.4
1994
310.2
1984
399.2
1995
290.5
1985
385.4
1996
266.3
1986
372.7
1997
248.3
1987
379.6
1998
217.4
1988
378.4
1999
198.0
1989
373.4
2000
197.3
1990
348.9
2001
186.2
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