Final answer:
The number of people in the town who have caught the flu after 4 weeks can be calculated by substituting t = 4 into the function N(t) = 12,000 / (1 + 999e^-t), following the steps, and rounding to the nearest person.
Step-by-step explanation:
The function N(t) = 12,000 / (1 + 999e-t) models the number of people in a small town who have caught the flu t weeks after the initial outbreak. To find out how many people have caught the flu after 4 weeks, we need to substitute t = 4 into the function and calculate the value.
Plugging in the value we get N(4) = 12,000 / (1 + 999e-4). Using a calculator to compute the exponential and division, we arrive at a number, which we will round to the nearest person as the question asks.
Here's the step-by-step calculation:
Calculate e-4.
Multiply 999 by e-4.
Add 1 to the result of step 2.
Divide 12,000 by the result of step 3.
Round the final number to the nearest person.