Question

How long will it take for the population of a certain country to double if its annual growth rate is 1.5%? Round to the nearest year. Use the exponential growth model P(t) = P0e^kt

Answer 1

Two ways to do it:
each year multiply by 1.015 (like compound interest)
1.015^n = 2
n log 1.015 = log 2
n = log 2 / log1.015 = 46.55 years

or do it the way they said to do it with continuous growth
dy/dt = .015y
y = yi e^.015 t
y/yi = 2 = e^.015 t
ln 2 = .015 t
t = 46.2