Suppose a population growth is modeled by the logistic equation $\frac { d P } { d t } = 0.01 P - 0.0001 P ^ { 2 }$ with P(0) = 10. Find the population after 500 years.
A)50
B)94
C)70
D)500
E)80
F)100
G)35
H)30

Question

Quizplus · Accepted Answer

The logistic equation $\frac { d P } { d t } = 0.01 P - 0.0001 P ^ { 2 }$ describes a population that grows initially and then stabilizes at a carrying capacity. Solving this differential equation with the initial condition P(0) = 10, the population approaches the carrying capacity over time. After 500 years, the population stabilizes close to the carrying capacity, which is 100, but slightly less due to the initial condition, resulting in approximately 94.

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 $\frac { d P } { d t } = 0.01 P - 0.0001 P ^ { 2 }$