Question

A population grows according to the logistic equation dp/dt = 0.04p − 0.0016p^2, where t is measured in weeks, and the initial population is p(0) = 10.

Answer 1

So, the particular solution to the logistic equation with the initial condition is:

`(1)/(0.04) ln |p| + (1)/(0.04) ln |1-0.004p |=t+(ln(6))/(0.04)`

This is the implicit solution to the logistic equation with the given initial condition. If you want the explicit form of

p(t), it may be necessary to use numerical methods or further algebraic manipulation.

Step-by-step explanation:

Answer 2

The given equation represents the population growth according to the logistic model, where the population growth rate slows down as the population reaches its carrying capacity.

Step-by-step explanation:

The given equation represents the population growth according to the logistic model. The equation is dp/dt = 0.04p - 0.0016p^2, where t is measured in weeks and p represents the population. The initial population is given as p(0) = 10. This equation represents logistic growth, where the growth rate initially increases but eventually slows down as the population reaches its carrying capacity.