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

1.	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.
Answer» Given, Initial production of scooters = 40000 Final production of scooters = 46305 Time duration = 3 years Let annual growth rate = R% So \(= 40000({1}+\frac{R}{100})({1}+\frac{R}{100})({1}+\frac{R}{100})\) = 46305 \(=({1}+\frac{R}{100})^3\) \(=\frac{46305}{40000}\) \(=\frac{9261}{8000}\) = \((\frac{21}{20})^3\) \(=1+\frac{R}{100}\) \(=\frac{21}{20}\) \(=\frac{R}{100}\) \(=\frac{21}{20}-1\) \(=\frac{1}{20}\) \(=R = \frac{1}{20}\times100\) = 5% Hence, Annual growth rate of production of scooters = 5 %

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.

Answer»

Given,

Initial production of scooters = 40000

Final production of scooters = 46305

Time duration = 3 years

Let annual growth rate = R%

\(= 40000({1}+\frac{R}{100})({1}+\frac{R}{100})({1}+\frac{R}{100})\) = 46305

\(=({1}+\frac{R}{100})^3\) \(=\frac{46305}{40000}\) \(=\frac{9261}{8000}\) = \((\frac{21}{20})^3\)

\(=1+\frac{R}{100}\) \(=\frac{21}{20}\)

\(=\frac{R}{100}\) \(=\frac{21}{20}-1\) \(=\frac{1}{20}\)

\(=R = \frac{1}{20}\times100\) = 5%

Hence,

Annual growth rate of production of scooters = 5 %