Solve the problem.
-The logistic growth functi $f ( t ) = \frac { 440 } { 1 + 6.3 e ^ { - 0.2 t } }$ 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) 60 butterflies
B) 440 butterflies
C) 6 butterflies
D) 880 butterflies

Question

Quizplus · Accepted Answer

The limiting size of the butterfly population is found by examining the logistic growth function as $t$ approaches infinity. The term $6.3e^{-0.2t}$ approaches 0 as $t$ becomes very large, leaving the function to approach $\frac{440}{1+0} = 440$. Therefore, the limiting size of the butterfly population the habitat will sustain is 440 butterflies.

Solve the Problem f(t)=4401+6.3e−0.2tf ( t ) = \frac { 440 } { 1 + 6.3 e ^ { - 0.2 t } }f(t)=1+6.3e−0.2t440​

Solve the Problem $f ( t ) = \frac { 440 } { 1 + 6.3 e ^ { - 0.2 t } }$