Problem
The function $N(t)=\frac{13,000}{1+999 e^{-t}}$ models the number of people in a small town who have caught the flu $t$ weeks after the initial outbreak. Step 1. How many people were ill initially? Round to the nearest person. (3.00 Points
Solution
Step 1 ：The function \(N(t)=\frac{13,000}{1+999 e^{-t}}\) models the number of people in a small town who have caught the flu \(t\) weeks after the initial outbreak.
Step 2 ：The initial number of people who were ill can be found by substituting \(t=0\) into the function. This is because the function models the number of people who have caught the flu \(t\) weeks after the initial outbreak, so at \(t=0\), this would represent the initial number of people who were ill.
Step 3 ：Substituting \(t=0\) into the function gives us \(N(0)=\frac{13,000}{1+999 e^{0}} = 13.0\)
Step 4 ：Final Answer: The initial number of people who were ill is \(\boxed{13}\).
