Doomsday Equation Consider the differential equation where K > 0 and In Section...

Doomsday Equation Consider the differential equation where K > 0 and In Section 3.1 we saw that in the case C = 0 the linear differential equation is a mathematical model of a population P(t) that exhibits unbounded growth over the infinite time interval See Example 1 on page 84.

(a) Suppose for that the nonlinear differential equation is a mathematical model for a population of small animals, where time t is measured in months. Solve the differential equation subject to the initial condition and the fact that the animal population has doubled in 5 months.

(b) The differential equation in part (a) is called a doomsday equation because the population exhibits unbounded growth over a finite time interval that is, there is some time T such

(c) From part (a), what is

(reference example 1)