MAT 112
Fall 2015
Print Name: __________________________
Departmental Final Exam - Version X
EKU ID: ______________________________
NON-CALCULATOR SECTION
Instructor: ___________________________
Calculators are NOT allowed on this part of the final. Show work to support each answer. Full
credit may not be awarded for questions without any work shown. Each question in this
section is worth 10 points.
1) Write the slope-intercept form of the equation for the line passing through the points
(9, 0) and (-2, 4).
2) Solve the formula A = P(1 + nr) for r.
3) Solve the system of equations, if a solution exists:
1
7x + 6y = 22
-4x - 3y = -10
4) John owns a hot dog stand. He has found that his profit is given by the equation
P(x) = -x2 + 64x + 73, where P(x) is the amount of profit when x hot dogs are sold. How
many hot dogs must he sell to earn the most profit?
5) Find the inverse of the function f(x) = 4x3 - 1.
4 2 2
-3 6 3
and B = -2 -8 8 . Compute AB, if possible.
6) A =
-2 3 -6
2 -7 -9
Final Exam, MAT 112, Fall 2015, Version X, page 2 of 7
Name: _________________________________
EKU ID: ________________________________
CALCULATOR SECTION. Calculators are allowed on this section.
MULTIPLE CHOICE. Choose the best answer. Circle the correct letter on the answer sheet, and
then fill in your circle. Each question in this section is worth 5 points.
7) Given f(x) = 2x2 + 3x - 3, find f(-4).
A) 32
B) 17
C) -23
D) 20
8) A cellular phone company determines a monthly bill from the x number of minutes of
usage. The amount of the bill, B(x), (in dollars) is given by the function:
B(x) = 29.97 + 0.12x. Determine the bill of a customer who uses her cellular phone
28.00 minutes during the month.
F) $33.33
G) $3.36
H) $842.52
J) $28.00
9) The population of a small town can be modeled by P = -32t + 12,800, where t is the
number of years since 2010. Interpret the slope of the graph of this function as a rate
of change.
A) The population of the town is decreasing by 32 people per year.
B) The population of the town is increasing by 12,800 people per year.
C) The population of the town is increasing by 32 people per year.
D) The population of the town is decreasing by 12,800 people per year.
10) An electrician charges a fee of $45 plus $30 per hour. Let y be the cost in dollars of
using the electrician for x hours. Find the slope-intercept form of the equation.
F) y = 45x + 30
G) y = 30x + 45
H) y = 45x - 30
J) y = 30x - 45
11) The temperature, t, in degrees Fahrenheit, of water being heated is 66 +
1
m where m
4
is the number of minutes since heating began. How long will it take for the
temperature of the water to reach 70 degrees Fahrenheit?
A) 13 min
B) 10 min
C) 32 min
D) 16 min
12) Jim has gotten scores of 64 and 92 on his first two tests. What score must he get on
his third test to keep an average of 85 or greater?
F) At least 80.3
G) At least 99
H) At least 98
J) At least 78
Final Exam, MAT 112, Fall 2015, Version X, page 3 of 7
13) The demand for a certain product is given by p + 6q = 304, and the supply is given by
p - 6q = 28, where p is the price in dollars and q is the quantity demanded or supplied
at price p. Find the price at which the quantity demanded equals the quantity
supplied.
A) $168
B) $169
C) $166
D) $163
14) Solve: z2 + 18z + 62 = 0.
F) z = 9 + 19
G) z = -18 + 62
H) z = 9 ± 62
J) z = -9 ± 19
15) Ten students in a graduate program were randomly selected. Their grade point
averages (GPAs) when they entered the program were between 3.5 and 4.0. The
following data were obtained regarding their GPAs on entering the program versus
their current GPAs. The linear model for this data is y = 3.67 + 0.0313x, where x is
entering GPA and y is current GPA. Use this model to predict current GPA of a student
whose entering GPA is 3.5.
Entering GPA Current GPA
3.5
3.6
3.8
3.7
3.6
3.9
3.6
3.6
3.5
3.9
3.9
3.8
4.0
3.7
3.9
3.9
3.5
3.8
3.7
4.0
A) 3.29
B) 3.58
C) 3.40
D) 3.78
16) The intensity of a radio signal from the radio station varies inversely as the square of
the distance from the station. Suppose the the intensity is 8000 units at a distance of
2 miles. What will the intensity be at a distance of 12 miles? Round your answer to the
nearest unit.
F) 248 units
G) 186 units
H) 205 units
J) 222 units
17) Write the equation of the quadratic function whose graph is a parabola containing the
points (0, 3), (3, 15), and (-3, 27).
A) y = 3x2 - 2x + 3
C) y = 2x2 + 2x +1
B) y = 2x2 - x + 3
D) y = 2x2 - 2x + 3
Final Exam, MAT 112, Fall 2015, Version X, page 4 of 7
18) Find (g
f)(-7) when f(x) =
F) -55
x-3
and g(x) = 7x + 4.
2
G) -31
H) 225
J) - 24
19) The difference between the tuition at State University and Highbrow College is less
than $1300. The tuition at Highbrow is $3500. Express this as an absolute value
inequality. Use "x" for the tuition of State University.
A) x < 2200
B) x > 3500 - 1300
C) x - 3500 < 1300
D) x - 1300 < 3500
20) Write the equation of the function g(x) that is transformed from f(x) = x , if the
graph of g is shown.
F) y = x
-3
G) y = x - 3
H) y = x + 3
J) y = x - 3 + 3
21) The growth in the population of a certain rodent at a dump site fits the exponential
function A(t)= 915e0.016t, where t is the number of years since 1985. Estimate the
population in the year 2000.
A) 1163
B) 582
C) 1182
D) 930
22) Given that loga11 = 2.398 and loga5 = 1.609, evaluate loga
F) 0.789
G) 1.49
11
.
5
H) -0.788
J) 4.007
23) Use a change of base formula to evaluate log 2 (0.697). Approximate to three decimal
places.
A) -0.521
B) -0.157
C) 2.869
D) -1.920
Final Exam, MAT 112, Fall 2015, Version X, page 5 of 7
24) Wind speed varies in the first twenty meters above the ground. For a particular day,
let f(x) = 1.2 ln x + 4.6 model the wind speed x meters above the ground. What is the
wind speed 11 meters above the ground? Round results to the nearest hundredth.
F) 7.48 meters per second
G) -1.72 meters per second
H) 6.43 meters per second
J) 7.00 meters per second
25) How long would it take $5000 to grow to $15,000 at 6% compounded continuously?
Round your answer to the nearest tenth of a year.
A) 18.9 years
B) 18.3 years
C) 18.5 years
D) 16.9 years
26) A couple who wants to purchase a home with a price of $275,000 has $50,000 for a
down payment. If they can get a 25-year mortgage at 7% per year, paid on the unpaid
balance, what is the total amount they will pay before they own the house outright?
How much interest will they pay over the life of the loan?
F) $583,092; $308,092
G) $477,075; $202,075
H) $633,092; $358,092
J) $527,075; $252,075
27) S(x) = -x3 + 6x2 + 288x + 4000, 4 x 20 is an approximation of the number of salmon
swimming upstream to spawn, where x represents the water temperature in degrees
Celsius. Find the temperature that produces the maximum number of salmon.
A) 12°C
B) 8°C
C) 20°C
D) 4°C
28) Some people must eat a low-sodium diet with no more than 2000 mg of sodium per
day. By eating 1 cracker, 1 pretzel, and 1 cookie, a person would ingest 149 mg of
sodium. If a person ate 8 pretzels and 8 cookies, he or she would ingest 936 mg of
sodium. By eating 6 crackers and 7 pretzels, a person would take in 535 mg of sodium.
Which of the following statements is true?
F) A cracker contains 30 mg of sodium.
G) A pretzel contains 49 mg of sodium.
H) A cookie contains 71 mg of sodium.
J) A cracker contains more sodium than a cookie.
29) Find the cubic function that models the data in the table.
x -5
0 2 3
y -60 5 3 10
A) y = 0.58x3 + 0.25x2 - 2.83x + 5.00
B) y = 0.49x3 - 0.25x2 + 2.83x + 5.00
C) y = 0.58x3 - 0.25x2 - 2.83x + 5.00
D) y = 0.49x3 - 0.25x2 - 2.83x + 5.00
Final Exam, MAT 112, Fall 2015, Version X, page 6 of 7
30) Solve: x3 + 3x2 - x - 3 = 0. List the solutions.
F) 1, -1, -4
G) 1, -1, -3
H) 1, -1, 3
31) Write the augmented matrix associated with the system
4 5 -2 21
A) 3 8 -2 29
6 6 2 22
4 5 -2
B) 3 8 -2
6 6 2
J) 1, -2, 5
4x + 5y - 2z = 21
3x + 8y - 2z = 29 .
6x + 6y + 2z = 22
4 3 6 21
C) 5 8 6 29
-2 -2 2 22
21 -2 5 4
D) 29 -2 8 3
22 2 6 6
32) The tables below give the number of points scored and rebounds gotten by the five
starters on a basketball team in the first two games of the season. Write a matrix
containing the total number of points and rebounds for each of the starting five.
Game 1 Points Rebounds
Levy
19
3
Cowens 16
5
Williams 8
12
Miller
3
11
Jenkins
10
2
37 7
28 8
F) 20 21
7 21
20 5
7 37
28 8
G) 21 20
21 7
5 20
Game 2 Points Rebounds
Levy
18
4
Cowens 12
3
Williams 12
9
Miller
4
10
Jenkins
10
3
H) 62 5
J) 5 62
33) Suppose a plumber charges $160 for the first hour plus $60 for each additional hour.
Write an expression for the cost (in dollars) of a job lasting n hours.
A) 220n
C) 160 + 60(n - 1)
34) Evaluate the sum:
B) 160 + 60n
D) 160 · 60n-1
4
i =1
F)
40
3
2+i
.
i
G)
20
3
H)
49
3
Final Exam, MAT 112, Fall 2015, Version X, page 7 of 7
J)
49
6