Question

The logistic growth function ​f(t)equals440 Over 1 plus 13.7 e Superscript negative 0.28 t EndFraction 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 20 ​months? Round to nearest whole number.

Answer 1

8685 butterflies

Explanation:

Given the logistics growth function expressed as ​f(t)equals440 Over 1 plus 13.7 e Superscript negative 0.28 t which describes the population of a species of butterflies t months after they are introduced to a​ non threatening habitat, to know the number of butterflies expected butterflies are expected in the habitat after 20 ​months, we will substitute t = 20 into the function.

f(20) = 440/1+13.7exp-(0.28×20)

f(20) = 440/1+13.7exp-(5.60)

f(20) = 440/1+(13.7× 0.003698)

f(20) = 440/1+0.05066

f(20) = 440/1.05066

f(20) = 8684.9

This means there will be approximately 8685 butterflies in the habitat after 20months.