Solve the problem.
-The logistic growth function $\mathrm { f } ( \mathrm { t } ) = \frac { 82,000 } { 1 + 2732.3 \mathrm { e } ^ { - 1.4 \mathrm { t } } }$ 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) 82,000 people
B) 164,000 people
C) 2732 people
D) 2733 people

Question

Quizplus · Accepted Answer

The limiting size of the population that becomes ill is found by taking the limit of the logistic growth function as $t$ approaches infinity. In this case, as $t$ approaches infinity, $e^{-1.4t}$ approaches 0, making the denominator approach 1. Thus, the limiting size is $\frac{82,000}{1} = 82,000$ people.

Solve the Problem f(t)=82,0001+2732.3e−1.4t\mathrm { f } ( \mathrm { t } ) = \frac { 82,000 } { 1 + 2732.3 \mathrm { e } ^ { - 1.4 \mathrm { t } } }f(t)=1+2732.3e−1.4t82,000​

Solve the Problem $\mathrm { f } ( \mathrm { t } ) = \frac { 82,000 } { 1 + 2732.3 \mathrm { e } ^ { - 1.4 \mathrm { t } } }$