Chapter 5.1, Problem 19E

Population and Exponential Growth Let $P\left(t\right)$ be the population (in millions) of a certain city $t$ years after $2015$, and suppose that $P\left(t\right)$ satisfies the differential equation. $P\text{'}\left(t\right)=0.01P\left(t\right),P\left(0\right)=2$.

a. Find a formula for $P\left(t\right)$.

b. What was the initial population, that is, the population in $2015$?

c. Estimate the population in $2019$.