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**Unformatted text preview: **Math 124 Exam I Fall 2008
Name: PID:
Section: Date:
INSTRUCTKONS:
1. Do not open this exam until you are instructed to do so. 2.
3. Fill in the information at the top of the page. You will need a pen or pencil. one calculator and booklet for the exam. Please
clear everything else from your desk. . Please look to the board for possible correction to this exam. . Show your work in the place provided. If you need additional space, use the backs of the exam pages. You must show all your work. Points may be Withdraw
for answers given without substantiation. . Place your answers in the boxes, where provided. . You will be given 50 minutes for this exam. J 1 2 j 3 3 4 5 l s 7
L[Maximum Points [14:] (12) i (16) I (18] {12) {8) 1 (12)
Actual Points ‘ 1 % l Question 11! Math 124 Exam 1 Fall 2003 1. (10+4214 points) A biologist went to a remote island for a ﬁeld trip and recorded
the population of a species of primates in the island throughout a decade. Later
on he drew a graph describing his record in a report. in the ﬁrst two year of his
trip, the population of the primates grew steadily so that the graph was increas—
ing in a linear fashion. However, since there was not enough food on the island,
the pace of the growth slowed down in the next three years. In this period, the graph is still increasing but concave down. Starting from the ﬁfth year, the pop«
ulation is saturated so that it becomes constant. (a) Redraw the biologists graph in the space provided below. (Hint: The exact height of the graph is not important as iong as it makes sense and the shape
is correct.) Population 012345678910 :10 Math 124 Exam 1 Fall 2008 2. [8+4:12 points) A waste collection. service charges $480 for 100 kg of waste per
month and $640 for 160 kg of waste per month. [3) Find a linear formula for the cost, C of waste coiiection as a function of the number of kiiograms of waste w. (b) What is the slope of the line? Give units and interpret your answer in terms
of the cost of waste collection. ( . E ,, -' ~a t - 3. (4+4+4+4=16 points) An object is dropped from a high place. The table shows
the distance d in feet tseconds after it is dropped. ,t‘_‘*t—‘. r
i 4 i 0.8 IIO’ft}.
idioms '!
a 1.2 I 1.6 ‘ 2 10.24 23.04 40.96 l 64 No credit without substantiation. for (a) and (b). (a) Is the distance d expected to be increasing or decreasing between t m 0 and
t: 2 ? Math 124 Exam I Fa112008 (b) Is the distance d expected to be concave up or concave down between t = O (c) What is the change in distance between In: 0.4: and r z 1.6? Give unit(s) and
interpret your answer in terms of the distance. (d) What is the average velocity between t = 0.4 and t 2 1.6? Give unit(s) and
interpret your answe, in terms of the distance. y-"vf
r i: ‘ I 1 {M 4. (12+6218 points) The ﬁxed cost of producing hats is $3,000 and the additional
cost per hat is $4 . Each hat sells for $16. (a) Find formulas for the cost function, C(q), and the revenue function, R(q).
Use your answer to ﬁnd the break—even point 40. M f _ 95"". Math 124 Exam. 1 Fall 2008 (‘0) Sketch a graph of C (q) and mm on the same axes and label the break—even
point. ' . 6 I f i 3 ' f ’ i i 3 q 18
0 100200 300400500 6007008009001000 5. (4+4+4:12 points) Determine Whether each of the following tables of values could
correspond to a linear function, an exponential function or neither. (a) (b) (c) 6. (44428 points) Mike deposited $1500 in his saving account at annual interest
4%, compounded annually. (a) Find a formula for the Value of Mike’s account t years after the deposit. Math 124 Exam 1 Fall 2008 (‘0) Convert the formula found in part a to base e. Kali? k 1:: (2 K (T) - 8. (8 points) To determine the age of antiques, anthropologists would determine
the amount of carbon-14 remaining in them. Carbon-14 is a radioactive sub—
stance with half life 5730 years. Find a formula for the amount, A mg, of carbon-
14 in a scroll If years since it has been made provided that the initial amount of
the carbon~14 in it 100 mg. “ d5 {9 M ...

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- Derivative, Convex function