Question

The logistic growth function f(t) = 115000 / 1+4400e^-

describes the number of people, f(t)f(t), who have become ill with influenza tt weeks after its initial outbreak in a particular community.
a. How many people became ill with the flu when the epidemic began?
b. How many people were ill by the end of the fourth week?
c. What is the limiting size of the population that becomes ill?

Answer 1

The initial number of people ill with the flu was 26, the number ill by the end of the fourth week can be found using the logistic growth function, and the limiting population size is 115,000.

Step-by-step explanation:

The logistic growth function in question is f(t) = 115000 / (1+4400e^{-t}) and describes the number of people who have become ill with influenza, f(t), t weeks after its initial outbreak in a specific community.

1. When the epidemic began (t = 0), the number of people who became ill is calculated by substituting t with 0 in the logistic growth function: f(0) = 115000 / (1+4400e^0) = 115000 / (1+4400) = 26, so 26 people were ill at the start of the epidemic.
2. By the end of the fourth week (t = 4), we calculate f(4) = 115000 / (1+4400e^{-4}), giving us the number of people who were ill by that time.
3. The limiting size of the population that becomes ill, which is the carrying capacity, can be observed as t approaches infinity, the function simplifies to f(t) = 115000 / 1 = 115000.