According to a census taken towards the end of the year 2009, the population of a rural town was found to be 64000. The census authority also found that the population of this particular town had a growth of 5% per annum. In how many years after 2009 did the population of this town reach 74088 ?

Let in n years population reaches from 64000 to 74088.

For growth :

Value after n year = Present value $\times \Big(1 + \dfrac{r}{100}\Big)^n$

Substituting values we get :

$\Rightarrow 74088 = 64000 \times \Big(1 + \dfrac{5}{100}\Big)^n \\[1em] \Rightarrow \dfrac{74088}{64000} = \Big(\dfrac{105}{100}\Big)^n \\[1em] \Rightarrow \dfrac{9261}{8000} = \Big(\dfrac{21}{20}\Big)^n \\[1em] \Rightarrow \Big(\dfrac{21}{20}\Big)^3 = \Big(\dfrac{21}{20}\Big)^n \\[1em] \Rightarrow n = 3.$

In 3 years the population will reach 74088.