Answer
a. 20 people
b. 1080 people
c. 100,000 people.
Work Step by Step
The logistic growth model: $A=\displaystyle \frac{c}{1+ae^{-bt}}$,
(a,b,c are constants and $c>0, b>0$)
describes situations in which growth is limited.
$y=c$ is a horizontal asymptote for the graph,
and growth, $A$, can never exceed $c$.
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$\mathrm{a}$.
$t=0$.
$ f(0)=\displaystyle \frac{100,000}{1+5000e^{0}}\approx$19.9960007998
20 people became ill when the epidemic began.
$\mathrm{b}.\ f(4)=\displaystyle \frac{100,000}{1+5,000e^{-4}}\approx$1080.16796613
(about 1080 people)
$\mathrm{c}$.
The limiting size of the population that become ill is given by c in the logistic growth model
c=100,000 (people).
