Solve the problem.
-The logistic growth function $f ( t ) = \frac { 600 } { 1 + 6.5 e ^ { - 0.18 t } }$ 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 12 months?
A) 343 butterflies
B) 960 butterflies
C) 601 butterflies
D) 7200 butterflies

Question

Quizplus · Accepted Answer

To find the expected number of butterflies after 12 months, substitute $t = 12$ into the logistic growth function and solve for $f(12)$:$$f(12) = \frac{600}{1 + 6.5e^{-0.18 \times 12}}$$$$= \frac{600}{1 + 6.5e^{-2.16}}$$$$= \frac{600}{1 + 6.5 \times 0.115}$$$$= \frac{600}{1 + 0.7475}$$$$= \frac{600}{1.7475}$$$$= 343.317...$$Therefore, the expected number of butterflies in the habitat after 12 months is approximately 343.

Solve the Problem f(t)=6001+6.5e−0.18tf ( t ) = \frac { 600 } { 1 + 6.5 e ^ { - 0.18 t } }f(t)=1+6.5e−0.18t600​

Solve the Problem $f ( t ) = \frac { 600 } { 1 + 6.5 e ^ { - 0.18 t } }$