A conservation organization releases 100 animals of an endangered species into a game preserve. The organization believes that the preserve has a carrying capacity of 900 Animals and that the growth of the herd will follow the logistic curve $p ( t ) = \frac { 900 } { 1 + 10 e ^ { - 0.1656 t } }$ where t is measured in months. What is the population after 8 Months? Round your answer to the nearest animal.
A) 23 animals
B) 243 animals
C) 159 animals
D) 308 animals
E) 246 animals

Question

A conservation organization releases 100 animals of an endangered species into a game preserve. The organization believes that the preserve has a carrying capacity of 900 Animals and that the growth of the herd will follow the logistic curve  $p ( t ) = \frac { 900 } { 1 + 10 e ^ { - 0.1656 t } }$ where t is measured in months. What is the population after 8 Months? Round your answer to the nearest animal.
A) 23 animals
B) 243 animals
C) 159 animals
D) 308 animals
E) 246 animals

Quizplus · Accepted Answer

To find the population after 8 months, substitute $t = 8$ into the given logistic growth equation: $p(t) = \frac{900}{1 + 10e^{-0.1656t}}$. This gives $p(8) = \frac{900}{1 + 10e^{-0.1656 \times 8}}$, which calculates to approximately 246 animals when rounded to the nearest whole number.

A Conservation Organization Releases 100 Animals of an Endangered Species p(t)=9001+10e−0.1656tp ( t ) = \frac { 900 } { 1 + 10 e ^ { - 0.1656 t } }p(t)=1+10e−0.1656t900​

A Conservation Organization Releases 100 Animals of an Endangered Species $p ( t ) = \frac { 900 } { 1 + 10 e ^ { - 0.1656 t } }$