The world population was 2560 million in 1950 and 6,080 million in 2000. assume the growth rate of the population p'(t) is proportional to the size of the population p(t): p'(t)=kp(t)

Let denote the population at time in millions.

The population's growth rate is modeled by the differential equation



This equation is separable, and we can solve easily:






Let's assume 1950 corresponds to year , so that 2000 would correspond to . Then , which means we have



and , which means





So the population is modeled by



(assuming refers to the year 1950)