SOLUTION: The logistic growth function f(x)=95,000/1+4749.0e^-1.3t models the number of people who have become ill with a particular infection t weeks after its intial outbreak in a particul

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Question 1096501: The logistic growth function f(x)=95,000/1+4749.0e^-1.3t models the number of people who have become ill with a particular infection t weeks after its intial outbreak in a particular community. What is the limiting size of the population that becomes ill? Show work.
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!

The logistic function is

f%28x%29=95000%2F%281%2B4749.0e%5E%28-1.3t%29%29

Every logistic function is of this form. The maximum value of the function is always the numerator of the fraction.
This is easily seen by considering what happens to the expression as t gets very large ("goes towards infinity").

As t gets larger, the expression e%5E%28-1.3t%29 gets smaller; in the limit as t goes to infinity, that expression goes to 0. Then the denominator of the becomes (in your example) 1%2B4749.0%2A0+=+1

And with the denominator going to 1, the numerator becomes the function value.

So the limiting size of the population that becomes ill in your example is 95,000.