The natural resources of an island limit the growth of the population. The population of the island is given by the logistic equation $\mathrm { P } ( \mathrm { t } ) = \frac { 4943 } { 1 + 3.96 \mathrm { e } ^ { - 0.31 t } }$ , where t is the number of years after 2010. What is the limiting value
Of the population?
A) 997 people
B) 1266 people
C) 4943 people
D) 14 people

Question

Quizplus · Accepted Answer

The limiting value of the population, according to the logistic equation, is the value of P(t) as t approaches infinity. As t becomes very large, the term $3.96e^{-0.31t}$ approaches 0, making the denominator approach 1. Thus, the limiting value of P(t) is 4943.

The Natural Resources of an Island Limit the Growth of the Population