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

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Note it does not matter that we multiplied through by 16 here because we need ... View the full answer