Answer
a. $20$ people.
b. $1080$ people.
c. $100,000$ people.
Work Step by Step
Given the model function $f(t)=\frac{100,000}{1+5000e^{-t}}$, we have:
a. At the beginning of the epidemic, $t=0$ and $f(0)=\frac{100,000}{1+5000e^{0}}=\frac{100,000}{5001}\approx20$ people.
b. At $t=4$ weeks, we have $f(4)=\frac{100,000}{1+5000e^{-4}}\approx1080$ people.
c. To find the limiting size, let $t\to\infty$, we have $5000e^{-t}\to0$; thus $f=100,000$ people.
