Suppose that a population grows according to a logistic model with carrying capacity 2,000 and $k = 0.05$ per year. Choose the logistic differential equation for these data.
A) $\frac { d P ( t ) } { d t } = P \left( 1 + \frac { p } { 2,000 } \right)$
B) $\frac { d P ( t ) } { d t } = 0.05 P \left( 1 + \frac { p } { 5 } \right)$
C) $\frac { d P ( t ) } { d t } = 2,000 P \left( 1 + \frac { p } { 0.05 } \right)$
D) $\frac { d P ( t ) } { d t } = 0.05 P \left( 1 + \frac { p } { 2,000 } \right)$
E) $\frac { d P ( t ) } { d t } = 0.05 P \left( 1 - \frac { p } { 2,000 } \right)$

Question

Quizplus · Accepted Answer

The logistic differential equation is given by $\frac { d P ( t ) } { d t } = k P \left( 1 - \frac { P } { K } \right)$, where $K$ is the carrying capacity and $k$ is the growth rate. Here, $K = 2000$ and $k = 0.05$, which matches option E.

Suppose That a Population Grows According to a Logistic Model k=0.05k = 0.05k=0.05

Suppose That a Population Grows According to a Logistic Model $k = 0.05$