In a factory the production of scooters rose to 46305 from 40000 in 3 years.

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 $5 \%$.

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