Question

the function $n(t) = \frac{14,000}{1 + 999e^{-t}}$ models the number of people in a small town who have caught the flu $t$ weeks after the initial outbreak. step 1 of 2: how many people were ill initially? round to the nearest person.

Explanation:

Step1: Identify initial time

Initially, \( t = 0 \) (at the start, 0 weeks after outbreak).

Step2: Substitute \( t = 0 \) into \( N(t) \)

Substitute \( t = 0 \) into \( N(t)=\frac{14000}{1 + 999e^{-t}} \). Since \( e^0 = 1 \), we get \( N(0)=\frac{14000}{1 + 999\times1} \).

Step3: Simplify the expression

Calculate denominator: \( 1 + 999 = 1000 \). Then \( N(0)=\frac{14000}{1000}=14 \).

Answer:

14