$\text { The logistic function } P ( t ) = \frac { 20 } { 1 + 0.5 e ^ { - 0.2 t } } \text { models the growth of a population. }$ Identify the maximum carrying capacity.
A)20
B)1.7
C)0.5
D)0.2
E)2.2

Question

Quizplus · Accepted Answer

The maximum carrying capacity is the horizontal asymptote of the logistic function, which is the value of $P(t)$ as $t$ approaches infinity. In this function, it is 20, as indicated by the numerator of the fraction.

The logistic function P(t)=201+0.5e−0.2t models the growth of a population. \text { The logistic function } P ( t ) = \frac { 20 } { 1 + 0.5 e ^ { - 0.2 t } } \text { models the growth of a population. } The logistic function P(t)=1+0.5e−0.2t20​ models the growth of a population.

$\text { The logistic function } P ( t ) = \frac { 20 } { 1 + 0.5 e ^ { - 0.2 t } } \text { models the growth of a population. }$