A factory increased its production of cars from 80000 in the year 2011-2012 to 92610 in 2014-2015. Find the annual rate of growth of production of cars.

Let rate of growth be r% per annum.

Growth formula,

V = $V_0\Big(1 + \dfrac{r}{100}\Big)^n$

Putting values in formula we get,

$\Rightarrow 92610 = 80000\Big(1 + \dfrac{r}{100}\Big)^3 \\[1em] \dfrac{92610}{80000} = \Big(1 + \dfrac{r}{100}\Big)^3 \\[1em] \dfrac{9261}{8000} = \Big(1 + \dfrac{r}{100}\Big)^3 \\[1em] \Big(\dfrac{21}{20}\Big)^3 = \Big(1 + \dfrac{r}{100}\Big)^3 \\[1em] 1 + \dfrac{r}{100} = \dfrac{21}{20} \\[1em] \dfrac{r}{100} = \dfrac{21}{20} - 1 \\[1em] \dfrac{r}{100} = \dfrac{21 - 20}{20} \\[1em] \dfrac{r}{100} = \dfrac{1}{20} \\[1em] r = \dfrac{100}{20} \\[1em] r = 5\%.$

Hence, the annual rate of growth of production of cars is 5%.