Question

A population P obeys the logistic model. It satisfies the equation dP/dt = 8/500 P(5-P) for P>0.

The population is increasing when ____ < P < ____

Answer 1

The logistic model for population growth is described by the equation dP/dt = (r/k)P(1 - P/k). To determine when the population is increasing, we need to find the range of values for P where dP/dt is positive. In this case, the population is increasing when 0 < P < 5.

Step-by-step explanation:

The logistic model for population growth is described by the equation
`dP/dt = (r/k)P(1 - P/k)` population, t represents time, r is the intrinsic growth rate, and K is the carrying capacity of the environment.

To determine when the population is increasing, we need to find the range of values for P where dP/dt is positive. In this case, the given equation is dP/dt = 8/500 P(5-P). Setting this expression greater than 0 and solving for P, we get:

8/500 P(5-P) > 0

Simplifying, we find that the population is increasing when 0 < P < 5.