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Mathematics
Problem
A rumor spreads through a town according to
d
R
d
t
=
0.3
R
(
1000
−
R
)
\frac{dR}{dt}=0.3R(1000-R)
d
t
d
R
=
0.3
R
(
1000
−
R
)
, where
R
(
t
)
R(t)
R
(
t
)
is the number of residents who have heard the rumor
t
t
t
hours after it begins. Determine the maximum number of people who can ever hear the rumor according to this model.
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