Loyola University Chicago
Department of Mathematics and Statistics
MATH 131 Applied Calculus I - Summer 2015
Instructor: Cristina Popovici
Tuesday, June 2, 2015
NAME (please print clearly):
Exam 1
Question 1 (15 points):
Question 2 (20 points):
Question 3 (15 points):
Question 4 (15 points):
Question 5 (15 points):
Question 6 (20 points):
TOTAL SCORE:
Notes:
1. You have 60 minutes to complete the exam.
2. For full credit you must show your work completely. Simply writing down an
answer without justifying it will receive very little partial credit.
3. NO TEXTBOOKS or NOTES are allowed while you take this exam.
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1. (15 points) Aircraft require longer takeoff distances, called takeoff rolls, at high
altitude airports because of diminished air density. The table shows how the takeoff
roll for a certain light airplane depends on the airport elevation. (Takeoff rolls are
also strongly influenced by air temperature; the data shown assume a temperature
of 0◦ C.) Determine a formula for this particular aircraft that gives the takeoff roll
as an exponential function of airport elevation.
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2. (20 points) The cost of producing q articles is given by the function
C = f (q) = 100 + 2q.
(a) Find a formula for the inverse function.
(b) Explain in practical terms what the inverse function tells you.
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3. (15 points) A culture of bacteria originally numbers 500. After 2 hours there are
1500 bacteria in the culture. Assuming exponential growth, how many bacteria are
there after 6 hours?
4
4. (15 points) Find a possible formula for the graph below.
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5. (15 points) According to Car and Driver, an Alfa Romeo going at 70 mph requires
177 feet to stop. Assuming that the stopping distance is proportional to the square
of velocity, find the stopping distance required by an Alfa Romeo going at 35 mph
and at 140 mph (its top speed).
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6. (20 points) In the graph of f in the figure below, at which of the labeled x-values
is
(a) f (x) greatest?
(b) f (x) least?
(c) f ′ (x) greatest?
(d) f ′ (x) least?
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