Activity 7.4.2.
Suppose that the population of a town is growing continuously at an annual rate of 3% per year.
(a)
Let \(P(t)\) be the population of the town in year \(t\text{.}\) Write a differential equation that describes the annual growth rate.
(b)
Find the solutions of this differential equation.
(c)
If you know that the town’s population in year 0 is 10,000, find the population \(P(t)\text{.}\)
(d)
How long does it take for the population to double? This time is called the doubling time.
(e)
Working more generally, find the doubling time if the annual growth rate is \(k\) times the population.
