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Mat 152 Final Exam 100% Correct Answers

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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
)

=
1296
b.

2

6

<
7
c.
3

3

4

2

12

+
16
=
0
d.
|


1
2
|
=
3
e.

3

2
+
4

2

=
0
f.
푙표푔
4
64
=
푥 g .
푙표푔
2

+
푙표푔
2
(


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.
1. Find the rate of change of profit for this product when between 150 and 250 units are sold.
1. 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

+
4


14

=
0
3

+
5

+

=
19

+
4



=
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

=
100
+
96


16

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”,

(

)
,
is between 1 and 10, with 10 being as physi cally fit as Tarzan and
1 being an utter and complete Mr. Couch Potato.

represents the number of weeks from the beginning of the semester. This scenario is modeled by the function

(

)
=
10

7
.
3
푙표푔
(

+
1
)
;
0



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
<


104
,
630
.

(

)
=
{
0
.
13

푖푓
0
<


39
,
600
5
,
148
.
00
+
0
.
21
(


39
,
600
)
푖푓
39
,
600
<


104
,
630
1. Use the function to find

(
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

(

)
=
18


3
, find the inverse of

(

)
.
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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