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Math 115 – First Midterm Exam
Solutions
Name:
Instructor:
Section Number:
1.
Do not open this exam until you are told to begin.
2. This exam has 8 pages including this cover. There are 8 questions.
3. Do not separate the pages of the exam. If any pages do become separated, write your name on them and
point them out to your instructor when you turn in the exam.
4. Please read the instructions for each individual exercise carefully. One of the skills being tested on this
exam is your ability to interpret questions, so instructors will not answer questions about exam problems
during the exam.
5. Show an appropriate amount of work for each exercise so that the graders can see not only the answer but
also how you obtained it. Include units in your answers where appropriate.
6. You may use your calculator. You are also allowed two sides of a 3 by 5 notecard.
7. If you use graphs or tables to obtain an answer, be certain to provide an explanation and sketch of the
graph to show how you arrived at your solution.
8. Please turn oF all cell phones and pagers and remove all headphones.
Problem
Points
Score
1
18
2
16
3
6
4
9
5
14
6
11
7
11
8
15
Total
100
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1. (18 points) The frst and only edition oF a certain calculus book came out in 1994. A partial
publisher’s record re±ecting the price
p
, in dollars, oF the book
t
years aFter it was frst published
is given below.
t
0
2
4
6
8
p
67
61
54
46
37
(Assume
p
and its derivative are di²erentiable Functions.)
(a) (5 pts.) Use the data to estimate
p
′
(6). Show your work; include units.
•
p
′
(6)
≃
p
37
−
46
2
+
46
−
54
2
P
1
2
=
p
−
9
2
+ (
−
4)
P
1
2
=
−
4
.
25 dollars per year.
(b) (4 pts.) Use your answers From part (a) to give a practical interpretation oF
p
′
(6). You should
only use everyday language that a noncalculus student would understand.
In 2000 the price oF the book was dropping by about 4 dollars and 25 cents per year.
(c) (3 pts.) You somehow fnd out that
p
′
(8) =
−
5
.
25. What is the most reasonable estimate oF
the price oF the book in 2003? Show brieF work.
•
p
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 Fall '08
 BLAKELOCK
 Math, Calculus

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