Math 131 Exam I Sample Questions Worksheet With Answer Key - Washington University Page 4
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616.
A female boll weevil can lay on average 200 eggs (source: North Carolina Department of Agriculture).
Suppose, for simplicity's sake, that each boll weevil results in 75 boll weevils the following year. Let
y be the number of boll weevils in a particular field in 1995.
a) Suppose there were only 2 boll weevils in a particular field in 1995. Give an exponential model for
y.
b) According to the model, how many boll weevils would be in that field in the year 2000?
17.
Your grandparents put aside $10,000 in an account, which earns 8% interest for your college, when you
were born.
a) How much would you have in the account in 18 years if interest was compounded monthly?
b) When would you have $40,000 in the account if the interest was compounded continuously?
=
−
+
18.
Describe how the graph of
y
2
f
(
x
) 3
4
differs from the graph of y = f(x).
=
−
+
−
19.
2
If
g
(
x
)
x
x
, find and simplify
g
(
x
h
)
g
(
x
)
.
−
=
20.
3
x
2
Determine functions f and g such that
f
(
g
(
x
))
e
. (Do not choose f(x) = x or g(x) = x.)
=
+
π
21.
The model
y
5
4
9 .
cos(
t
)
represents the water level y in feet at Padre Island t hours after midnight.
6
a) Find the range of the water level at Padre Island.
b) Find the period of this function to find the amount of time between high tides.
c) How high is the water level at 1:30pm according to the model?
22.
The population in country A is 40 million on January 1, 1990 and increases by 6% each year thereafter.
The population in country B is 60 million on January 1, 1990 and increases by 4% each year thereafter.
How long will it take for the population in country A to surpass the population in country B?
23.
A local bank is offering a savings account with an annual interest rate of 5.69% compounded quarterly.
What should be the annual interest rate of an account whose interest is compounded continuously, but
which has the same effective annual yield?
24.
If the population of the world was 2.564 billion in 1950 and the annual population growth rate was
1.85%, find an exponential equation to model the population of the world as a function of time (since
1950). According to your model, during what year will the population first reach 7 billion?
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