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MATH 111B
Exam I October 19, 2006
Name
Student ID # Section
HONOR STATEMENT
“I affirm that my work upholds the highest standards of honesty and academic integrity at the University of Washington, and that I have neither given nor received any unauthorized assistance on this exam.”
SIGNATURE:
Total 50
- Please check that your exam contains 3 problems.
- Please turn your cell phone OFF and put it away for the duration of the exam.
- Unless otherwise indicated, you must show your work. Clearly label lines and points that you are using and show all calculations. The correct answer with no supporting work may result in no credit.
- Put your name on your sheet of notes and turn it in with the exam.
GOOD LUCK!
- (16 points) You produce and sell Things. The graph below shows your total cost (T C).
0
5,
10,
15,
20,
25,
30,
35,
40,
45,
0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000
dollars
quantity (in Things)
TC
(a) What is the variable cost (V C) of producing 5000 Things?
ANSWER: $
(b) What is the smallest value of average cost (AC)?
ANSWER: $ per Thing (c) Estimate the change in total cost that occurs when quantity increases from 1000 to 1001 Things.
ANSWER: $
(d) If items sell at a market price of $6 each, name the largest quantity at which T R = T C.
ANSWER: q = Things
- (17 points) A counter at the gate of an airport parking lot keeps track of the number of cars that have come into the lot since 10 a.m. Another counter keeps track of the number of cars that have left the lot since 10 a.m. The two graphs below show the number that have come in and gone out over a fifteen-hour period. Let C(t) represent the number of cars in the lot t hours after 10 a.m. The lot contains 2500 cars at 10 a.m. (That is, C(0) = 2500.)
0
500
1000
1500
2000
2500
3000
3500
4000
4500
5000
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
cars
time (in hours since 10 a.m.)
out
in
in out
(a) Translate the following statement into English and then decide if it is true or false:
C(6) > C(7).
TRANSLATION:
(circle one) true false (b) Name the first time at which the overall rate of flow in is the same as the overall rate of flow out.
ANSWER: t = hours after 10 a.m. (c) Find a one-hour interval during which at least 500 cars entered the lot.
ANSWER: from t = to t = (d) On average, how many cars left the lot per hour during the five-hour interval starting at 10 a.m.?
ANSWER: cars per hour
