In many population growth problems, there is an upper limit beyond which the population cannot grow. many scientists agree that the earth will not support a population of more than 16 billion. there were 2 billion people on earth in 1925 and 4 billion in 1975. if is the population years after 1925, an appropriate model is the differential equation
dy/dt=ky(16-y)

note that the growth rate approaches zero as the population approaches its maximum size. when the population is zero then we have the ordinary exponential growth described by y'=16ky. as the population grows it transits from exponential growth to stability.

(a) solve this differential equation.
(b) the population in 2015 will be
(c) the population will be 9 billion some time in the year