Assume that the population of a city satisfies the logistic hypothesis:
"The rate of change of population at any time is proportional to the product of the population at that time and the difference between capacity and population."
We have the following data: capacity is 11,825,000, population in 1960 was 3,750,500, and population in 2000 was 4,215,500.
(a) Set up and solve an Initial Value Problem to express the population of the city as a function of time.
(b) Draw a graph of the population.
(c) Calculate an estimate of the population in the year 2030.