Question

Suppose the population of a town is 100,000 in 1999. The population increases at a rate of 4.5% every year. What will be the population of the town in 2005. Round answer to the nearest whole number.

Answer 1

let P be the initial population, r is the rate for every year
in 1 year = P+P(r) = P(1+r)
now the current population is P(1+r)
in 2 years= P(1+r)+P(1+r)r = P(1+r)(1+r) = P(1+r)^2
and it goes on the same way..
from 99 to 2005 = 6 years
then you have P(1+r)^t where:
P=100,000
r=4.5/100=0.045
t=6