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Homework 1/28
1. A population of critters is measured by the function
P
(
t
) = 100(2
t/
5
)
where
t
is measured in years and
P
is measured in critters.
(a) Graph
P
(
t
) on the domain 0
≤
t
≤
15 years. Be sure to label your graph correctly.
(b) Find the
rate of
change of
P
on the interval 3
≤
t
≤
5 years. Correct units are required.
(c) Repeat for the intervals:
i. [4
,
5]
ii. [5
,
6]
iii. [5
,
7]
(d) In your graph from part (a), sketch secant lines whose slopes match these four rates of
change.
(e) Compute the rate of change of
P
on the interval [5
, a
].
2. The position of a moving object is measured by the function
s
(
t
) = 2 sin(
π
(
t

0
.
5))
where
t
is measured in minutes and
s
is measured in feet.
(a) Graph
s
(
t
) on the domain 0
≤
t
≤
4 minutes. Be sure to label your graph correctly.
(b) Find the rate of change of
s
(with units) on each of the intervals:
i. [0
,
1]
ii. [
.
5
,
1]
iii. [1
,
1
.
5]
iv. [1
,
2]
v. [1
, a
]
(c) Sketch secant lines for the ±rst four rates.
3. The voltage in a circuit is given by
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 Spring '08
 STAFF
 Calculus

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