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 at the start of 1925 and 4 billion at the beginning of 1975. If $y$ is the population, measured in billions, $t$ years after 1925, an appropriate model is the differential equation $$\frac{dy}{dt} = ky(16-y).$$ 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. $y =$
(b) The population in 2015 will be $y =$ billion.
(c) The population will be 9 billion some time in the year

Note that the data in this problem are out of date, so the numerical answers you'll obtain will not be consistent with current population figures.
Hint: (a) Separate variables and use the given information to solve for $y$. (b) Evaluate $y$. (c) Solve for the appropriate time.