Question

The population of a suburb is 16000. Find the rate of increase in the population if the population after two years is 17640.

Answer 1

Here, P = Population of a suburb = 16000
A = Population after two years =17640
R = R %
N = 2 years

$$\begin{gathered} \mathrm{A}=\mathrm{P}{\left(1+\frac{\mathrm{R}}{100}\right)}^{\mathrm{N}} \\ \Rightarrow 17640=16000{\left(1+\frac{\mathrm{R}}{100}\right)}^2 \\ \Rightarrow \frac{17640}{16000}={\left(1+\frac{\mathrm{R}}{100}\right)}^2 \\ \Rightarrow \frac{441}{400}={\left(1+\frac{\mathrm{R}}{100}\right)}^2 \\ \Rightarrow {\left(\frac{21}{20}\right)}^2={\left(1+\frac{\mathrm{R}}{100}\right)}^2 \\ \Rightarrow 1+\frac{\mathrm{R}}{100}=\frac{21}{20} \\ \Rightarrow \frac{\mathrm{R}}{100}=\frac{21}{20}-1 \\ \Rightarrow \frac{\mathrm{R}}{100}=\frac{1}{20} \\ \Rightarrow \mathrm{R}=5 \end{gathered}$$

Hence, the rate of increase in the population is 5 p.c.p.a.