Question

the function n(t)=\frac{50,000}{1 + 20e^{-2.5t}} describes the number of people, n(t), who become ill with a virus t weeks after its initial outbreak in a town with 50,000 inhabitants. the horizontal asymptote in the graph indicates that there is a limit to the epidemics growth. complete parts (a) through (c) below.
a. how many people became ill with the virus when the epidemic began? (when the epidemic began, t = 0.)
when the epidemic began, approximately
(round to the nearest person as needed.)

Explanation:

Step1: Substitute t = 0 into the function

We have the function $N(t)=\frac{50000}{1 + 20e^{-2.5t}}$. When $t = 0$, we substitute $t$ into the function: $N(0)=\frac{50000}{1+20e^{-2.5\times0}}$.
Since $e^{-2.5\times0}=e^{0}=1$, the function becomes $N(0)=\frac{50000}{1 + 20\times1}$.

Step2: Calculate the value of N(0)

First, calculate the denominator: $1+20\times1=1 + 20=21$.
Then, $N(0)=\frac{50000}{21}\approx2381$.

Answer:

2381