Answer
a.$f(0)=200$
b.$f(6)=45410.7282$,
c. $500, 000$
Work Step by Step
$f(t)=\frac{500000}{1+2499e^{-0.92t}}$
a. When the epidemic first begins, $t=0$,
$f(0)=\frac{500000}{1+2499}=200$
b. By the end of the sixth week, $t=6$,
$f(6)=\frac{500000}{1+2499e^{-0.92\times6}}=45410.7282$
c. When $t\rightarrow \infty$, $e^{0.92t}\rightarrow 0$, therefore
$f(t)=\dfrac{500,000}{1+e^{-90.92t}}\rightarrow \dfrac{500,000}{1}=500,000$
Therefore, the limiting size is $500, 000$.
