The Function F(T)=575,000/1+4000e^-T

Question

describes the number of people, F(T) , who have become ill with ebola

T weeks after the initial outbreak in a particular community.

How many people became ill with ebola when the epidemic began?

How many people were infected 6 weeks after the initial breakout? Round to the nearest whole number of people?

What is the limiting size of the infected population? That is, how many people were infected at t = (infinity sign goes after = sign)? Round to the nearest whole number of people.

Answer 1

Your notation is a bit ambiguous, but I'm guessing the function is:

f(t) = 575,000 / (1 + 4000e^-t )

How many people became ill with Ebola when the epidemic began? Set t = 0 and use your calculator to compute the answer.

How many people were infected 6 weeks after the initial breakout? Set t = 6 and use your calculator to compute the answer. As instructed, round to the nearest whole number of people.

What is the limiting size of the infected population? That is, how many people were infected at t = ∞?

As t --> ∞, 4000e^-t --> 0, so plug 0 in for 4000e^-t and figure out the answer. As instructed, round to the nearest whole number of people.