Exploding population (10 points). Records of the world’s human population, it has been claimed, in-

dicate that the growth rate of the population is not constant, but rather proportional to the population

size itself. This means that the rate of growth is kp(t), where p(t) denotes the world population (num-

ber of living humans) at year t, and k: is a constant. Population records suggest that k z 4.1 x 10—12.

The differential equation describing this model is dp_ _ 2

a—(kpM—kp- (a) Find the general solution to this equation. (b) Find the particular solution that also satisﬁes the condition that the current population is M2018) =

7.6 x 109. Ic) Show that there is a time when the population will become inﬁnite. At which year will the

pepulation explosion happen according to this model? Math