Choose the one alternative that best completes the statement or answers the question.
-The logistic growth function $\mathrm { f } ( \mathrm { t } ) = \frac { 440 } { 1 + 7.8 \mathrm { e } ^ { - 0.17 \mathrm { t } } }$ describes the population of a species of butterflies $\mathrm { t }$ months after they are introduced to a non-threatening habitat. How many butterflies were initially introduced to the habitat?
A) 2 butterflies
B) 50 butterflies
C) 8 butterflies
D) 440 butterflies

Question

Quizplus · Accepted Answer

The initial population is found by evaluating the logistic growth function at $t = 0$. Substituting $t = 0$ into the function gives $\mathrm { f } ( 0 ) = \frac { 440 } { 1 + 7.8 \mathrm { e } ^ { - 0.17 \times 0 } } = \frac { 440 } { 1 + 7.8 } = \frac { 440 } { 8.8 } = 50$. Therefore, 50 butterflies were initially introduced to the habitat.

Choose the One Alternative That Best Completes the Statement or Answers