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Section 1.1 Version 1
1. A ball is tossed upward from a tall building, and its upward velocity V, in feet per
second, is a function of the time t, in seconds, since the ball was thrown. The formula is
V = 40 − 32t, if we ignore air resistance. The function V is positive when the ball is
rising and negative when the ball is falling. Using the functional notation of velocity
calculate the velocity of a ball 0.4 second after it is thrown. Is the ball rising or falling
then?
A)
B)
C)
D)
E)
V(0.4) = –29.20 feet per second, falling
V(0.4) = 31.20 feet per second, rising
V(0.4) = 20.00 feet per second, falling
V(0.4) = 27.20 feet per second, rising
V(0.4) = 16.00 feet per second, rising
2. A ball is tossed upward from a tall building, and its upward velocity V, in feet per
second, is a function of the time t, in seconds, since the ball was thrown. The formula is
V = 40 − 32t, if we ignore air resistance. The function V is positive when the ball is
rising and negative when the ball is falling. By how much does the velocity change from
4 to 5 seconds after the ball is thrown?
A)
B)
C)
D)
E)
The velocity is changing by 34.00 feet per second.
The velocity is changing by 17.50 feet per second.
The velocity is changing by –36.00 feet per second.
The velocity is changing by –32.00 feet per second.
The velocity is changing by 27.00 feet per second.
3. Earthquakes can result in various forms of damage, but many result in fault ruptures, or
cracks in the Earth's surface. In a 1958 study of earthquakes in California and Nevada,
D. Tocher found the following relationship between the fault rupture length L, in
kilometers, and the magnitude M (on the Richter scale) of an earthquake:
L = 0.0000017 × 10.47M.
What fault rupture length would be expected from an earthquake measuring 8.00 on the
Richter scale? Round your answer to the nearest hundredth.
A)
B)
C)
D)
E)
14541.29 km
245.48 km
2454.84 km
154.51 km
232.66 km
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4. When a breeding group of animals is introduced into a restricted area such as a wildlife
reserve, the population can be expected to grow rapidly at first but to level out when the
population grows to near the maximum that the environment can support. Such growth
is known as logistic population growth, and ecologists sometimes use a formula to
describe it. Suppose the number N of deer present at time t (measured in years since the
herd was introduced) on a certain wildlife reserve can be determined by the function
17.4
N =
. How many deer were initially on the reserve? (Round your answer
0.06 + 0.44t
to the nearest unit.)
A)
B)
C)
D)
E)
5.
35
42
300
17
16
If f (r, s, t) =
A)
B)
C)
D)
E)
r + 3 s + 2 t , calculate f (196, 150, 58).
15.43
25.03
20.75
15.46
15.32
6. The function T ( P, r , m ) gives the time required to pay off an installment loan of P
dollars if the APR is r as a decimal and we make monthly payments of m dollars. Use
functional notation to indicate the time required to pay off a $10000 automobile loan at
an APR of 6% if the monthly payment is $430.
A)
T (10000, 0.06, 430 )
B)
T (10000, 6, 430 )
C)
T ( 0.06,10000, 430 )
D)
T ( 430,10000, 0.06 )
E)
T ( 6, 430,10000 )
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7. The apparent magnitude m of a star is a measure of its apparent brightness as the star is
viewed from Earth. Larger magnitudes correspond to dimmer stars, and magnitudes can
be negative, indicating a very bright star. For example, the brightest star in the night sky
is Sirius, which has an apparent magnitude of −1.45. Stars with apparent magnitude
greater than about 6 are not visible to the naked eye. The magnitude scale is not linear
in that a star that is double the magnitude of another does not appear to be twice as dim.
Rather, the relation goes as follows: If one star has an apparent magnitude of m1 and
another has an apparent magnitude of m2, then the first star is t times as bright as the
second, where t is given by t = 2.512m2 − m1 . If a star has an apparent magnitude of 3.4,
how many times brighter than this star does Sirius appear? Round your answer to two
decimal places.
A)
B)
C)
D)
E)
46.91
6.03
87.12
47.32
34.68
8. When a breeding group of animals is introduced into a restricted area such as a wildlife
reserve, the population can be expected to grow rapidly at first but to level out when the
population grows to near the maximum that the environment can support. Such growth
is known as logistic population growth, and ecologists sometimes use a formula to
describe it. Suppose the number N of deer present at time t (measured in years since the
herd was introduced) on a certain wildlife reserve can be determined by the function
12.6
N =
. Calculate N(14).
0.69 + 0.77t
A) 176
B) 18
C) 19
D) 32
E) 2
9. A ball is tossed upward from a tall building, and its upward velocity V, in feet per
second, is a function of the time t, in seconds, since the ball was thrown. The formula is
V = 40 − 32t, if we ignore air resistance. The function V is positive when the ball is
rising and negative when the ball is falling. Describe the flight of the ball from 1.48
seconds on.
A) constantly rising after 1.48 seconds
B) rising from 1.48 seconds until 1.80 seconds and then falling constantly after 1.80
seconds
C) rising from 1.48 seconds until 2.20 seconds and then falling constantly after 2.20
seconds
D) rising from 1.48 seconds until 2.92 seconds and then falling constantly after 2.92
seconds
E) constantly falling after 1.48 seconds
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Answer Key
1.
2.
3.
4.
5.
6.
7.
8.
9.
D
D
B
E
E
A
C
B
E
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