Solve the problem.
-The population of wolves in a state park after $\mathrm { t }$ years is modeled by the function $\mathrm { P } ( \mathrm { t } ) = \frac { 500 } { 1 + 99 \mathrm { e } ^ { - 0.3 \mathrm { t } } }$. What is the maximum number of wolves possible in the park?
A) 5
B) 1000
C) 99
D) 500

Question

Quizplus · Accepted Answer

The maximum number of wolves is determined by the horizontal asymptote of the function, which is the value of $P(t)$ as $t$ approaches infinity. In this case, as $t$ approaches infinity, $99e^{-0.3t}$ approaches 0, making the denominator approach 1. Thus, the maximum number of wolves $P(t)$ approaches is $500/1 = 500$.

Solve the Problem t\mathrm { t }t Years Is Modeled by the Function

Solve the Problem $\mathrm { t }$ Years Is Modeled by the Function