Suppose a population growth is modeled by the logistic equation $\frac { d P } { d t } = 0.01 P - 0.0001 P ^ { 2 }$ . What is the carrying capacity?
A)90
B)10
C)50
D)1000
E)100
F)60
G)20
H)10,000

Question

Quizplus · Accepted Answer

The carrying capacity in a logistic growth model is determined by setting the growth rate to zero and solving for $P$. The logistic equation given is $\frac { d P } { d t } = 0.01 P - 0.0001 P ^ { 2 }$. Setting $\frac { d P } { d t } = 0$, we get $0 = 0.01 P - 0.0001 P ^ { 2 }$. Rearranging, $0.0001 P ^ { 2 } = 0.01 P$, which simplifies to $P = \frac{0.01}{0.0001} = 100$. Therefore, the carrying capacity is 100.

Suppose a Population Growth Is Modeled by the Logistic Equation dPdt=0.01P−0.0001P2\frac { d P } { d t } = 0.01 P - 0.0001 P ^ { 2 }dtdP​=0.01P−0.0001P2

Suppose a Population Growth Is Modeled by the Logistic Equation $\frac { d P } { d t } = 0.01 P - 0.0001 P ^ { 2 }$