Mat 122 Fall 2011 - Homework #4 Solutions Worksheet With Answer Key
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6MAT 122 Fall 2011
Overview of Calculus
Homework #4 Solutions
Problems
• Section 1.9: 4, 10, 14, 18, 24, 30
• Section 2.1: 6, 10, 16, 18
• Section 2.2: 4, 10, 22, 24, 28
3
p
1.9.4. Determine if y
is a power function, and if it is, write it in the form kx
and
8x
give the values of k and p.
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3
1
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3
1
Solution: We have that y
x
, so this is a power function, with k
8x
8
x
8
8
and p
1.
3
p
1.9.10. Determine if y
5x
is a power function, and if it is, write it in the form kx
and give the values of k and p.
3
3
3
3
Solution: We have that y
5x
5
x
125x
, so this is a power function, with
k
125 and p
3.
1.9.14. Write a formula for the energy, E, expended by a swimming dolphin, which is
proportional to the cube of the speed, v, of the dolphin.
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3
Solution: The energy E is proportional to v
, so E
kv
for some constant k.
2/3
1.9.18. The surface area of a mammal, S, satisfies the equation S
kM
, where M
is the body mass, and the constant of proportionality k depends on the body shape of
2
the mammal. A human of body mass 70 kilograms has surface area 18,600 cm
. Find
the constant of proportionality for humans. Find the surface area of a human with body
mass 60 kilograms.
2/3
Solution: From the data given, 18,600
k 70
, so
18,600
k
1095.1.
2/3
70
2/3
2/3
Then the surface area of a 60-kilogram human is S
k 60
1095.1 60
2
16,784 cm
.
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