Math 131 Exam I Sample Questions Worksheet With Answer Key - Washington University Page 3
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610.
The number of bacteria (in millions) in a bottle of milk after t days is given in the table below:
day
0
1
2
3
4
# of bacteria present
500
561
630
707
793
=
kt
Determine a formula of the form
Q
Q
e
that gives the number of bacteria present, Q (in millions),
0
as a function of t days. If the milk cannot be safely consumed when the bacteria count is greater than
3 billion per bottle, how many days will the bottle of milk be safe to drink?
11.
Suppose f, g, and h are functions of x such that one of them is proportional to x, one is inversely
proportional to x, and one is proportional to the square of x. Using the table below, write
f, g, and h as functions of x and find the constants of proportionality:
x
f(x)
g(x)
h(x)
5
600
50
1.25
10
300
200
2.50
15
200
450
3.75
20
150
800
5.00
25
120
1250
6.25
=
−
+
−
12.
2
The profit function for a skateboard company is given by
P
(
x
)
x
70
x
125
, where x is
the price charged by the company for a skateboard.
a) Find the price that will maximize profits.
b) For what prices will the company make a profit?
13.
What nominal interest rate has an effective annual yield of 5% under continuous compounding?
Round the percent to 2 places.
14.
An animal skull still has 20% of the carbon-14 that was present when the animal died. The half-life
of carbon-14 is 5730 years. Find the approximate age of the skull (to the nearest year).
15.
The depth of water in a tank oscillates once every 6 hours around an average depth of 7 feet.
If the smallest depth is 5.5 feet and the largest depth is 8.5 feet, find a formula for the depth in terms
of time, measured in hours. Assume the water level starts at 5.5 feet.
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