Solve the problem.
-The logistic growth function $\mathrm { f } ( \mathrm { t } ) = \frac { 320 } { 1 + 4.3 \mathrm { e } ^ { - 0.21 \mathrm { t } } }$ describes the population of a species of butterflies t months after they are introduced to a non-threatening habitat. How many butterflies were initially introduced to the habitat?
A) 60 butterflies
B) 320 butterflies
C) 4 butterflies
D) 2 butterflies

Question

Quizplus · Accepted Answer

The initial population is found by evaluating the logistic function at $ t = 0 $. Substituting $ t = 0 $ into the function gives $ f(0) = \frac{320}{1 + 4.3 \cdot e^0} = \frac{320}{1 + 4.3} = \frac{320}{5.3} \approx 60 $.

Solve the Problem f(t)=3201+4.3e−0.21t\mathrm { f } ( \mathrm { t } ) = \frac { 320 } { 1 + 4.3 \mathrm { e } ^ { - 0.21 \mathrm { t } } }f(t)=1+4.3e−0.21t320​

Solve the Problem $\mathrm { f } ( \mathrm { t } ) = \frac { 320 } { 1 + 4.3 \mathrm { e } ^ { - 0.21 \mathrm { t } } }$