Solve the problem.
-The logistic growth function $f ( t ) = \frac { 65,000 } { 1 + 3249.0 e ^ { - 1.4 t } }$ models the number of people who have become ill with a particular infection $t$ weeks after its initial outbreak in a particular community. What is the limiting size of the population that becomes ill?
A) 65,000 people
B) 130,000 people
C) 3249 people
D) 3250 people

Question

Quizplus · Accepted Answer

The limiting size of the population that becomes ill is given by the carrying capacity of the logistic growth function, which is the value of $f(t)$ as $t$ approaches infinity. In this function, $f(t) = \frac{65,000}{1 + 3249.0e^{-1.4t}}$, the carrying capacity is 65,000 people, as the exponential term goes to 0 when $t$ becomes very large, leaving $f(t) = \frac{65,000}{1}$.

Solve the Problem f(t)=65,0001+3249.0e−1.4tf ( t ) = \frac { 65,000 } { 1 + 3249.0 e ^ { - 1.4 t } }f(t)=1+3249.0e−1.4t65,000​

Solve the Problem $f ( t ) = \frac { 65,000 } { 1 + 3249.0 e ^ { - 1.4 t } }$