Project 12
MAC 2311
1. A sociologist determines that the percentage of a population that has heard a rumor
t
days
after the rumor begins to circulate (
t
= 0
) is given by
R
(
t
) =
100
t
2
20 +
t
+
t
2
What is the domain of
R
(
t
)
in this context? Calculate
R
(0)
and
lim
t
→∞
R
(
t
)
. Do your answers
make sense?
Calculate
dR
dt
, simplify, and factor. Does the derivative ever change sign for
t
≥
0
?
What is the initial rate of change of
R
(
t
)
with respect to
t
? (Include units.) How can this be?
What percentage of the population has heard the rumor after one day? What is the rate of
change of
R
(
t
)
with respect to
t
at that time? (Include units; round to the nearest tenth.)
How many days pass before forty percent of the population has heard the rumor? ﬁfty per
cent? What is the rate of change of
R
(
t
)
with respect to
t
at those time? (Include units.)
Of the times examined above, what was the general trend (up and down) of the
rate
at which
the rumor is spread? Brieﬂy explain why you think this might be true about the spread of a
rumor.
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View Full Document2. A population (in thousands) of black bears in a national park is represented by the function
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 Spring '08
 ALL
 Calculus

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