The logistic growth function at right describes the number of people, f(t), who have become ill with influenza t weeks after its initial outbreak in a particular community. f (t )equals startfraction 107 comma 000 over 1 plus 4200 e superscript negative t endfraction.
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?

Part (a): 25 people became ill with the flu when the epidemic began.

Part (b): 1373 people were ill by the end of the fourth week.

Part (c): The limiting size of the population that becomes ill is 107,000.

Step-by-step explanation:

Consider the provided logistic growth function

Part (a) How many people became ill with the flu when the epidemic began?

Substitute t = 0 in above function.

Hence, 25 people became ill with the flu when the epidemic began.

Part (b) How many people were ill by the end of the fourth week?

Substitute t = 4 in above function.

Hence, 1373 people were ill by the end of the fourth week.

Part (c) What is the limiting size of the population that becomes ill?

Substitute t = ∞ in above function.

Hence, the limiting size of the population that becomes ill is 107,000.

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