Question

The population of the world in 1987 was 5 billion and the annual growth rate was
estimated at 2 percent per year. Assuming that the world population follows an
exponential growth model, find the projected world population in 2015.

Answer 1

Assume formula
Population in billions at time t (counting from 1987) as
P(t)=Ae^(kt)
where A and k are constants.
At t=0 (1987),
P(0)=Ae^(0)=A=5
the formula becomes:
P(t)=5e^(kt)
P(1)=5*1.02=5e^(kt) [t=1]
=>
e^(k)=1.02 [t=1]
Take log both sides
k=log(1.02) [natural log]

So
P(t)=5e^(t*log(1.02))
where log(1.02)=0.0198 approx.