Using the concept of net rate introduced in Problem 2, determine a model for a populatio...

Using the concept of net rate introduced in Problem 2, determine a model for a population P(t) if the birth rate is proportional to the population present at time t but the death rate is proportional to the square of the population present at time t.

(reference problem 2)

The population model given in (1) fails to take death into consideration; the growth rate equals the birth rate. In another model of a changing population of a community it is assumed that the rate at which the population changes is a net rate—that is, the difference between the rate of births and the rate of deaths in the community. Determine a model for the population P(t) if both the birth rate and the death rate are proportional to the population present at time