Chapter 9.1, Problem 63E

The function

$N\left(t\right)=\frac{30,000}{1+20e^{-1.5t}}$

describe the number of people, $N\left(t\right)$, who become ill with influenza $t$ weeks after its initial outbreak in a town with 30,000 inhabitants. The horizontal asymptote in the graph indicates that there is a limit to the epidemic’s growth.

How many people became ill with the flu when the epidemic began? (When the epidemic began, $t=0$.)

How many people were ill by the end of the third week

Why can’t the spread of an epidemic simply grow indefinitely? What does the horizontal asymptote shown in the graph indicate about the limiting size of the population that becomes ill?