Choose the one alternative that best completes the statement or answers the question.
-The logistic growth function $f ( t ) = \frac { 800 } { 1 + 9.0 \mathrm { e } ^ { - 0.16 t } }$ describes the population of a species of butterflies $t$ months after they are introduced to a non-threatening habitat. How many butterflies are expected in the habitat after 15 months?
A) 801 butterflies
B) 1,200 butterflies
C) 440 butterflies
D) 12,000 butterflies

Question

Quizplus · Accepted Answer

To find the expected number of butterflies after 15 months, substitute $t = 15$ into the logistic growth function and solve for $f(15)$:$$f(15) = \frac{800}{1 + 9.0e^{-0.16 \times 15}}$$$$= \frac{800}{1 + 9.0e^{-2.4}}$$$$= \frac{800}{1 + 9.0 \times 0.09071795328941247}$$ (using a calculator for $e^{-2.4}$)$$= \frac{800}{1 + 0.8162614796055123}$$$$= \frac{800}{1.8162614796055123}$$$$= 440.53$$Rounding to the nearest whole number, the expected number of butterflies after 15 months is approximately 440.

Choose the One Alternative That Best Completes the Statement or Answers