The population of a city increases by 5% annually. If its population in 2010 was 138915 then, What it was in 2007 ?
Solution :
=138915 / (1 + 5%)^3
=138915 / (1 + 5 / 100)^3
=138915 x ( 20 / 21 x 20 / 21 x 20 / 21 )
= 120000.
I need to understand this (1 + 5%)^3 How is this derived. Any proof..?
Let $x$ be the population in $2,007$, then:
the population in $2,008$ is: $x(1+.05)$,and in $2,009$ is: $x(1+.05)(1+.05)$, and in $2,010$ is: $x(1+.05)(1+.05)(1+.05) = 138,915$. This explains the above analysis.