Answer
a)$$200$$
b)$$45411$$
c)$$500000$$
Work Step by Step
a) When the epidemic began, $t=0$, the number of ill people is$$f(0)=\frac{500000}{1+2499e^{(-0.92)(0)}}=200.$$
b) By the end of the sixth week, $t=6$, the number of ill people is$$f(6)=\frac{500000}{1+2499e^{(-0.92)(6)}} \approx 45411.$$
c) The number of ill people at the limiting size of $f(t)$, $t \to \infty$, tends to as follows:$$e^{-0.92t} \to 0 \quad \Rightarrow \quad f(t)=\frac{500000}{1+2499e^{-0.92t}} \to 500000$$
