Name ______________________
date
Dec 2010
section or days & time:
MATH 1090
FINAL EXAM
instructor:
.
2 hours with calculator
.
Work problems completely, either on this paper, or on another sheet, which you include with this paper.
Credit will be given for work, so show all necessary work. If you turn in work on another paper, number the
problems so they can be found and read. If you answer “none of the preceding,” tell what the answer should be.
Work 15 of the18 problems on this exam. Mark out the 3 problems
that will not be graded. The first 15 not marked out will be scored.
1. A certain piece of machinery was purchased five years ago for $750,000. Its present resale
value is $450,000. Assuming that the machine’s resale value decreases exponentially, what
will it be worth five years from now?
a) $210,000
b) $150,000
c) $270,000
d) $300,000
e) $0
f ) None of the preceding.
2. A private investment club has $200,000 earmarked for investment in stocks. To arrive at an
acceptable overall level of risk, the stocks are categorized as high risk, medium risk, or low
risk. Management estimates that the high-risk stocks will have a 15%/year rate of return,
medium-risk will have a 10%/year return, and low-risk stocks will have a 6%/year rate of
return. The members have decided that the investment in low-risk stocks should be equal to
the sum of the investments in the stocks of the other two categories. Determine how much the
club should invest in each type of stock if the investment goal is to have a return of
$20,000/year on the total investment. Assume that all the money available for investment is
invested.
a) $50,000 high risk, $50,000 medium risk, $100,000 low risk
b) $40,000 high risk, $40,000 medium risk, $120,000 low risk
c) $20,000 high risk, $80,000 medium risk, $100,000 low risk
d) $80,000 high risk, $20,000 medium risk, $100,000 low risk
e) $40,000 high risk, $60,000 medium risk, $100,000 low risk
f ) None of the preceding.
2
3. Find the tangent line to the graph of
at any point.
a)
b)
c)
d)
e)
f ) None of the preceding.
4. The total cost incurred by time t in the production of a certain commodity is f (t) dollars. The number of
products produced by time t is g (t). What does the function
represent?
a) The average production cost per product at time t.
b) The average number of products produced at time t.
c) The average production cost at time t.
d) The time t to produce a given production rate of production.
e) The total production cost at time t.
f ) None of the preceding.
5. The supplier of the Luminar desk lamp will make x thousand units of the lamp available
in the marketplace if its unit price is p dollars, where p and x are related by the equation
p = 0.1x2 + 0.5x + 15. If the unit’s price of the lamp is $20, how many units will the
supplier make available in the marketplace?
a) 2,500
b) 5,625
c) 14,375
d) 10,000
e) 5,000
f ) None of the preceding.
6. Andrea, a self-employed individual, wishes to accumulate a retirement fund of $250,000.
How much should she deposit each month into her retirement account, which pays interest at
the rate of 8.5%/year compounded monthly, to reach her goal upon retirement 25 years from
now?
a) $2,013.07
b) $1,498.88
c) $3,177.92
d) $242.23
e) $525.48
f ) None of the preceding.
3
7. A division of the Winston Furniture Company manufactures dining tables and chairs. Each table
requires 40 board feet of wood and 3 labor-hours. Each chair requires 16 board feet of wood
and 4 labor-hours. The profit for each table is $45, and the profit for each chair is $20. In a
certain week, the company has 3200 board feet of wood available, and 520 labor-hours. How
many tables and chairs should Winston manufacture in order to maximize profits?
a) 40 tables, 100 chairs
b) 0 tables, 130 chairs
c) 45 tables, 25 chairs
d) 25 tables, 45 chairs
e) 100 tables, 40 chairs
f ) None of the preceding.
8. The American Music program put on by the Mountain View Elementary School band charged
$1.50 for each regular adult and $1.00 for each senior (65 years and older). Children were free.
The seniors were each asked to donate $8 above the admission price to support the band, while
the other adults were asked to donate $12, and of course they all donated to help the kids. The
school only received $35 from the admissions, but it received $560 from the additional donations.
How many regular adults and how many seniors attended the music program?
a) 2 seniors, 22 adults
b) 5 seniors, 20 adults
c) 14 seniors, 14 adults
d) (35 – 1.5x) seniors, x adults
e) no solution
f ) None of the preceding.
9. Simplify
using positive exponents only.
a)
b)
c)
d)
e)
f ) None of the preceding.
10. Gift cards have increased in popularity in recent years. Consumers appreciate gift cards because they
get to select the present they like. The U.S. sales of gift cards (in billions of dollars) is approximated
by S(t) = –0.6204t3 + 4.671t2 + 3.354t + 47.4, (0 ≤ t ≤ 5) in year t, where t = 0 corresponds to 2003.
What were the sales of gift cards in 2008?
4
11. Find all the values of x for which
is continuous.
12. If you are considering leasing an auto for 2 years at $450 a month, and the money is worth 9%
compounded monthly, what is the equivalent cash payment (present value) for this annuity?
13.
The concentration of a drug in an organ at any time t (in minutes) is given be x(t) = 0.1 + 1.5e–0.08t,
g
where x(t) is measured in grams per cubic centimeter ( /cm3). How long would it take for the
g
concentration of the drug to reach 0.8 /cm3?
14. The Cinema Center consists of four theaters:
cinemas I, II, III, and IV. The attendance
for the Sunday matinee is given in the
adjacent matrix
Cinema I
Cinema II
Cinema III
Cinema IV
Children
225
75
280
0
Students
110
180
85
250
Adults
50
225
110
225
The prices are:
a. Write the matrix multiplication that gives the total
revenue for each cinema.
Children
4.00
b. Use the multiplication to find the total revenue for each cinema.
15.
The adjacent graph shows the volume of wood produced
in a single-species forest. Here f (t) is measured in cubic
meters per hectare and t is measured in years. By
computing the slope of the tangent line, estimate the rate
at which the wood grown is changing at the beginning of
the third year.
prices ($)
Students
6.00
.
Adults
8.00
5
16.
Determine graphically the solution of x + y ≤ 4
2x + y ≤ 6
2x – y ≥ –1
x ≥ 0, y ≥ 0
17.
The Venus Health Club for Women provides its members with the adjacent
table which gives the average desirable weight (in pounds) for women of a
given height (in inches). Find the linear function w(h) that predicts the
desirable weight for a given height.
18.
The parents of a child have just come into a large inheritance and wish to establish a trust fund for
her education. If they estimate that they will need $100,000 in 13 years, how much should they
set aside in the trust now if they can invest the money at 8½ % per year compounded quarterly?
Height, h
(inches)
60
63
66
69
72
Weight, w
(pounds)
108
118
129
140
152
*** ***
Formulas:
 (1 + i ) n − 1 
S = R

i


S = P(1 + r)
sn =
t
n ( a1 + an )
2
S = Pe
rt
 r
S = P 1 + 
 k
kt
1 − (1 + i )− n 
A= R

i


a1 ( 1 − r n )
sn =
(if r ≠ 1)
1− r
an = a1 + (n – 1)d
a n = a 1r n – 1
6
Answers — Math 1090, Final Exam, Fall 2010
1. sect’n 3.3, #6, C
2. sect’n 5.2, #58, D
3. sect’n 9.3, #14, E
4. sect’n 2.4, #56, A
5. sect’n 1.8, #78, E
6. sect’n 4.3, #31, D
7. sect’n 6.3, #33, A
8. sect’n 5.3, #33, D
9. sect’n 1.5, #47, A
10. sect’n 2.7, #10, $103,395,000,000
11. sect’n 9.2, #54, (- ∞, ∞)
12. sect’n 4.2, #23, $9850.12
13. sect’n 3.2, #69, 9.5 min
14. sect’n 5.5, #46,
15. sect’n 9.3, #2, 1 cubic meter per hectare per year
16. sect’n 6.1, #32, ⇒ graph ⇒
17. sect’n 2.2, #62, w(h) = 3.67h – 112.6
18. sect’n 4.1, #55, $33,506.76