Chapter 5.1, Problem 23E

Using the Differential Equation Let $P(t)$ be the population (in millions) of a certain city $t$ years after $2015$, and suppose that $P(t)$ satisfies the differential equation.

a. $P\text{'}(t)=.03P(t),P(0)=4$

b. Use the differential equation to determine how fast the population is growing when it reaches $5$ million people.

c. Use the differential equation to determine the population size when it is growing at the rate of $400,000$ people per year.

Find a formula for $P(t)$.