Solve the problem.
-The logistic growth functi $f ( t ) = \frac { 24,000 } { 1 + 599.0 \mathrm { e } ^ { - 1.8 t } }$ 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) 599 people
B) 24,000 people
C) 600 people
D) 48,000 people

Question

Quizplus · Accepted Answer

The limiting size of the population that becomes ill is the horizontal asymptote of the logistic growth function, which is the value of the function as $t$ approaches infinity. In the given function $f(t) = \frac{24,000}{1 + 599.0e^{-1.8t}}$, as $t$ approaches infinity, $e^{-1.8t}$ approaches 0, making the function approach $\frac{24,000}{1 + 0} = 24,000$. Therefore, the limiting size of the population that becomes ill is 24,000 people.

Solve the Problem f(t)=24,0001+599.0e−1.8tf ( t ) = \frac { 24,000 } { 1 + 599.0 \mathrm { e } ^ { - 1.8 t } }f(t)=1+599.0e−1.8t24,000​

Solve the Problem $f ( t ) = \frac { 24,000 } { 1 + 599.0 \mathrm { e } ^ { - 1.8 t } }$