The population of a colony was 3600 three years back. It is 4800 right now. What will be the population three years down the line, if the rate of growth of population has been co stant over the years and has been compounding annually?
(a)6000
(b)6400
(c)7200
(d)9600
Answer
Answer (as printed): B
Explanation
Let the rate of growth be R\% per annum. Then, $3600\left(1+\frac{\mathrm{R}}{100}\right)^{3}=4800 \Rightarrow\left(1+\frac{\mathrm{R}}{100}\right)^{3}=\frac{4}{3}$. $$\begin{aligned} \therefore \quad \text { Population after 3 years } & =4800\left(1+\frac{R}{100}\right)^{3} \\ & =4800 \times \frac{4}{3}=6400 . \end{aligned}$$
Explanation as extracted from the printed page; notation may be imperfect.