Suppose that a population grows according to a logistic model with carrying capacity 7,000 and $k = 0.05$ per year. Choose the logistic differential equation for these data.
A) $\frac { d P ( t ) } { d t } = 7,000 P \left( 1 + \frac { p } { 0.05 } \right)$
B) $\frac { d P ( t ) } { d t } = P \left( 1 + \frac { p } { 7,000 } \right)$
C) $\frac { d P ( t ) } { d t } = 0.05 P \left( 1 + \frac { p } { 7,000 } \right)$
D) $\frac { d P ( t ) } { d t } = 0.05 P \left( 1 + \frac { p } { 5 } \right)$
E) $\frac { d P ( t ) } { d t } = 0.05 P \left( 1 - \frac { p } { 7,000 } \right)$

Question

Quizplus · Accepted Answer

The logistic differential equation for population growth with carrying capacity $K$ and growth rate $k$ is $\frac{dP}{dt} = rk\left(1 - \frac{P}{K}\right)$. Substituting the values given in the problem, we get $\frac{dP}{dt} = (0.05)(P)\left(1 - \frac{P}{7,000}\right)$, which is equivalent to choice 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 $k = 0.05$