In the logistic model for population growth, $\frac { d P } { d t } = P ( 8 - 2 P )$ , the carrying capacity of the population $P ( t )$ is
A) 8
B) 2
C) 4
D) $1 / 4$
E) 16

Question

Quizplus · Accepted Answer

The carrying capacity in a logistic growth model is the value of $P$ at which the growth rate $\frac{dP}{dt}$ becomes zero. Setting the equation to zero, $0 = P(8 - 2P)$, solving for $P$ gives $P = 4$, which is the carrying capacity.

In the Logistic Model for Population Growth dPdt=P(8−2P)\frac { d P } { d t } = P ( 8 - 2 P )dtdP​=P(8−2P)

In the Logistic Model for Population Growth $\frac { d P } { d t } = P ( 8 - 2 P )$