Solve the problem.
-The logistic growth function $f ( t ) = \frac { 440 } { 1 + 5.3 e ^ { - 0.29 t } }$ 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 determined by the carrying capacity of the habitat, which is the maximum population size that the environment can sustain indefinitely. In the logistic growth function $f(t) = \frac{440}{1 + 5.3e^{-0.29t}}$, the carrying capacity is represented by the coefficient of the numerator, which is 440. This means the limiting size of the butterfly population the habitat will sustain is 440 butterflies.

Solve the Problem f(t)=4401+5.3e−0.29tf ( t ) = \frac { 440 } { 1 + 5.3 e ^ { - 0.29 t } }f(t)=1+5.3e−0.29t440​

Solve the Problem $f ( t ) = \frac { 440 } { 1 + 5.3 e ^ { - 0.29 t } }$