Suppose that a population develops according to the logistic equation
$$\frac { d P } { d t } = 0.04 P - 0.0004 P ^ { 2 }$$
where $t$ is measured in weeks. What is the carrying capacity? Select the correct answer.
A) $K = 0.04$
B) $K = 400$
C) $K = 0.0004$
D) $K = 100$
E) $K = 500$

Question

Quizplus · Accepted Answer

The logistic equation is given by $$\frac { d P } { d t } = r P \left( 1 - \frac { P } { K } \right)$$ where $r$ is the growth rate and $K$ is the carrying capacity. Comparing this with the given equation, we have $r=0.04$ and $-0.0004P$ corresponds to $-\frac{r}{K}P^2$, which implies $$\frac{r}{K}=0.0004.$$ Solving for $K$ we get $K=\frac{r}{0.0004}=100$. Therefore, the carrying capacity is 100, which is option D.

Suppose That a Population Develops According to the Logistic Equation dPdt=0.04P−0.0004P2\frac { d P } { d t } = 0.04 P - 0.0004 P ^ { 2 }dtdP​=0.04P−0.0004P2

Suppose That a Population Develops According to the Logistic Equation $\frac { d P } { d t } = 0.04 P - 0.0004 P ^ { 2 }$