Math 115 – First Midterm Exam
February 6, 2007
Name:
Instructor:
Section Number:
1.
Do not open this exam until you are told to begin.
2. This exam has 9 pages including this cover. There are 9 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 off all cell phones and pagers and remove all headphones.
Problem
Points
Score
1
16
2
9
3
12
4
13
5
12
6
16
7
7
8
7
9
8
Total
100
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2
1. According to a survey by the UM Transportation Research Institute, gasoline prices are projected
to reach $5.00 a gallon by the year 2020.
(a) (5 points) Assuming that the average gas price in 2007 is $2.00 per gallon (yes, we know
that is wishful thinking), find an exponential function,
P
, that models the average gas price
t
years after 2007. Show either an “exact” answer or at least 4 decimal places in your answer.
(b) (2 points) What is the
annual
percent change in the average gas price according to this
model? (Show to at least one decimal place.)
(c) (2 points) What is the yearly
continuous
percent rate of change for this model? (Show to
two decimal places.)
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