Question:
In a factory the production of scooters rose to 46305 from 40000 in 3 years. Find the annual rate of growth of the production of scooters.
Solution:
Let the annual rate of growth be $R$.
$\therefore$ Production of scooters after three years $=\mathrm{P}\left(1+\frac{\mathrm{R}}{100}\right)^{\mathrm{n}}$
$46,305=4,000\left(1+\frac{\mathrm{R}}{100}\right)^{3}$
$(1+0.01 \mathrm{R})^{3}=\frac{46,305}{40,000}$
$(1+0.01 \mathrm{R})^{3}=1.157625$
$(1+0.01 \mathrm{R})^{3}=(1.05)^{3}$
$1+0.01 \mathrm{R}=1.05$
$0.01 \mathrm{R}=0.05$
$\mathrm{R}=5$
Thus, the annual rate of growth is $5 \%$.