Solve the problem.
-The logistic growth model $P ( t ) = \frac { 410 } { 1 + 40 e ^ { - 0.176 t } }$ represents the population of a species introduced into a new territory after t years. When will the population be 60?
A) 10.94 years
B) 6.34 years
C) 3.69 years
D) 16.76 years

Question

Quizplus · Accepted Answer

To find when the population will be 60, we set $P(t) = 60$ and solve for $t$. Substituting 60 into the logistic growth model gives:$$60 = \frac{410}{1 + 40e^{-0.176t}}$$Solving this equation for $t$ involves isolating $e^{-0.176t}$, then taking the natural logarithm to solve for $t$. Following the algebraic steps leads to $t \approx 10.94$ years.

Solve the Problem P(t)=4101+40e−0.176tP ( t ) = \frac { 410 } { 1 + 40 e ^ { - 0.176 t } }P(t)=1+40e−0.176t410​

Solve the Problem $P ( t ) = \frac { 410 } { 1 + 40 e ^ { - 0.176 t } }$