Suppose that a population develops according to the logistic equation
$$\frac { d P } { d t } = 0.02 P - 0.0002 P ^ { 2 }$$
where $t$ is measured in weeks. What is the carrying capacity?
A) $K = 100$
B) $K = 0.02$
C) $K = 0.0002$
D) $K = 300$
E) $K = 200$

Question

Quizplus · Accepted Answer

The carrying capacity is the value of $P$ when $\frac { d P } { d t } = 0$. So we solve the equation $0.02 P - 0.0002 P ^ { 2 } = 0$. Factoring, we get $0.02 P (100 - P) = 0$. So either $P = 0$ or $P = 100$. Since $P = 0$ is not a valid solution, the carrying capacity is $K = 100$.

Suppose That a Population Develops According to the Logistic Equation dPdt=0.02P−0.0002P2\frac { d P } { d t } = 0.02 P - 0.0002 P ^ { 2 }dtdP​=0.02P−0.0002P2

Suppose That a Population Develops According to the Logistic Equation $\frac { d P } { d t } = 0.02 P - 0.0002 P ^ { 2 }$