Solve the problem.
-The logistic growth function $f ( t ) = \frac { 440 } { 1 + 5.3 e ^ { - 0.24 t } }$ describes the population of a species of butterflies t months after they are introduced to a non-threatening habitat. What is the limiting size of the butterfly population that the habitat will sustain?
A) 440 butterflies
B) 70 butterflies
C) 5 butterflies
D) 880 butterflies

Question

Quizplus · Accepted Answer

The limiting size of the butterfly population 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, $f(t) = \frac{440}{1 + 5.3e^{-0.24t}}$, as $t$ approaches infinity, $e^{-0.24t}$ approaches 0, making the function approach $f(t) = \frac{440}{1 + 0} = 440$. Therefore, the limiting size of the butterfly population the habitat will sustain is 440 butterflies.

Solve the Problem f(t)=4401+5.3e−0.24tf ( t ) = \frac { 440 } { 1 + 5.3 e ^ { - 0.24 t } }f(t)=1+5.3e−0.24t440​

Solve the Problem $f ( t ) = \frac { 440 } { 1 + 5.3 e ^ { - 0.24 t } }$