Question

The annual rate of growth in population of a certain city is $8\%$. If its present population is 196830, what it was 3 years ago?

Answer 1

Let 3 years ago, the population of a city = P
Rate of growth (R) $=8\%$ p.a.
Present population (P) = 196830
Period (n) = 3 years
$\because A=P{(1+\frac{R}{100})}^n$
$\Rightarrow P=A÷{(1+\frac{8}{100})}^3$
$=196830÷(1+\frac{2}{25}{)}^3$
$=196830÷{\left(\frac{27}{25}\right)}^3=196830\times {\left(\frac{25}{27}\right)}^3$
$=196830\times \frac{25}{27}\times \frac{25}{27}\times \frac{25}{27}$
$=10\times 25\times 25\times 25\therefore P=156250$
$\therefore$ 3 years ago, population of the city = 156250