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Unformatted text preview: Math 124 Exam 1 (10:20 AM) Fall 2008 Name: Section #: PID: Date: 9/15/2008 Instructions: 1. DO NOT OPEN THIS EXAM UNTIL YOU ARE INSTRUCTED TO DO SO. 2. Without fully Opening the exam, check that you have pages 1 through 7 and that none is
blank. 3. Fill the information at the top of the page. 4. Neither books nor scratch paper are needed for this exam. Clear your desk of everything
but this booklet, your pencils and your calculator. If you need more space to write your
solutions, use the backs of the exam pages. 5. Crib sheets (pre compiled lists of formuias or other information) either written or in a
calculator are speciﬁcally forbidden Use of a crib sheet ofany kind on this exam will
result' in an automatic zero grade. ' ' ' 6. The problems on this exam vary in difﬁculty. You should try to solve these problems 111 an order that will maximize your score. Solve all the easier problems first, then go back to
the ones that require more thought. 7. Unless otherwise indicated, SHOW ALL YOUR WORK. If no work is shown, no
partial credit can be awarded. Even for calculator solutions, you should include relevant inﬁirmatfon, like the equation to be solved, the function whose graph is to be sketched,
etc. 8. Please place your answers in the hoxes provided. 9. Unless you are speciﬁcally instructed to do otherwise, DO NOT ROUND YOUR
ANSWER. 10. You will be given exactly 55 minutes for this exam. I have read and fully understood all of the above instructions Signature: Points 1 E
Maximum '13 i 17 l 18 L16 l 14 Math 124 Exam 1 (10:20 AM) Fall 2008
it a xii i i . M
1. ( '3¢“6ﬂ'0%%t5) The number of sales per month, S is a function of the amount a, (in dollars) spent on advertising that month. So S=f(a) ' i
a) lnte 000)23500 ‘ J c . ,7
iii 3 . i x2... A? f“: s/aiif/iﬂiﬂt 3Z1 Z I)??? {3 Q” {9/ it
E ; a
#72. ‘ 0‘5 “i b) Suppose the number of sales is an increasing function ofthéioncy spent on
advertising, but how it increases depends on the amount of the money, For the ﬁrst
3000 dollars spent on advertising, the number of sales increases in a concave up style
while the sales increases in a linear style for the next 2000 dollars. Finally, after 5000
dollars has already spent on advertising, the sales function increases in a concave down style. Please sketch the sales function f(a) below according to the description
above. s
rnoe[
eoee ' '  ' ' ‘ /,~<”
soon
4000 i
i
i
i scoot (”do ..n .— m. (F
i i r r 1 l r?" a
0 1000 2000 3000 4000 5000 5000 7000' 8000 Give the domain and the range of the sales function you sketched above. Math 124 Exam 1 {10:20 AM) Fall 2808 2. (5+6+6&17 pts) Sales of music compact disks (CD3) increased rapidly throughout the
19905. Saies were 500 million CDs in 1994 and 938 million CD3 in 2000.
a) Find a linear formula for CD sales, S, as a function of the number ofthc years, r,
since 1991 (Where I = 0 corresponds to 1991.) ' c) What is the vertical intercept of the line found in part (21)? Give units with your
answer and interpret it. b.) Math 124 Exam 1 (10:20 AN!) Fall 2008 3. (4+4+4+6=l 8 pts)The following tables shows the population of Japan from 1985 to 2000
.Use the table to answer the fotlowing questions. 2000 2005 Population , , 125 570 126 926 E27 768
in thousands , . ii) If? m,” r {,4 i * " 5y? 1..
a) What is the Change/"r 1n the popuiatioh from 1985 to 1995”? Please give units. as} / :9 l l t? x20 M i‘ J b) Through 1985 to 2005 13 the population of Japan increasing??
{6’ ., Air’j / {:3 MT?” 9‘35 /f U” C) Find. the average rate of change of the population from 1985 and i995? Give units and
interpa'et your answer. "x d} Which ofthe following types of functions best ﬁts the above data?
Give reasons for you answer? a) Concave up
”Emit: r d
L)» oneave own
0) Linear Math 1124 Exam 1 (10:20 AM) Fail 2008 4. (4+4+3+5 = 16 points) A pillow making company has ﬁxed costs of $7500 and variable
costs of $2.5 per pillow. The company soils the pillows for $7 per pillow. Let g be the
number of pillows. . a) Find formulas for the cost function, C(q), and the revenue function, R(q). "3: ,... 4 2',” ,1"! {2&0 l ,i n ;( “J { 1w“ X “1:: W},
..X r. If;
F Cf , n  J L41"
\k Uri“1"” " j .i/ Win“ ’ f K ,. "’ 1,
k .\ 4,}; ,. ﬂ 3, /:
5 r f”
f L0 3 'x K ﬂ; F M5}
,) [ R), W , j
(’3 / jig/UM)
:jf c) What is the marginal cost and marginal proﬁt? d) Sketch a graph of C(q) and Rn?) on the same axes with an appropriate scale label axes
and the bicalooven point. “3"“ ' , l l 1 Wit" ! a
L i 1?, 242% ﬂint /
l TA ,, s S “i __
,L__L;_T LWLEEMW /
‘1' tin, All
_ , i 1.: :
3' 03¢“ «: Math 124 Exam 1 (10:20 AM) Fall 2008 5. (4 + 10=14 pts) For each ofthe following tables,
a.) determine which fuzmtion is linear and which function is exponential. (Make sure to Show
your work.) b.) Find the formulas for the linear and the exponential funetion(s) only. “”“C: L/ 3:33 / z r g a a?»
J” ".1" I. I? D ’ j § 3/. ‘ . {WM 1“ r 1' A W}; Math 124 Exam 1 (19:20 AM) Fall 2008 6. (Spts) Solve for t using natural logarithms: 7  2r = 10  3£
I. 5 may _ '1: j V: a 2...
ci‘unction m ihc form P 3 Pee” . What is thé 7. (Spts) For the functionP 3 33(13)’, puét 11 growth rate? 8. (5+7:12 pts) Suppose SB! 000 is invested in an account paying interest compounded
continuously at an annual rate of 9%. Find the following:
a) Find a formula for the value ofthc account at time t. ...
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