Question

The production of the factory increases every year by $5\%$. At present, the production is $160000$ tons. After how many years will the production reach $194481$ tons?

Answer 1

Present production : $P=160000,R=5$%

$P^{\prime }=$Production after $T$ years $=194481$ , So $T=?$

$P^{\prime }=P{(1+\frac{R}{100})}^T=\frac{194481}{160000}={\left(\frac{21}{20}\right)}^T={\left(\frac{21}{20}\right)}^4={\left(\frac{21}{20}\right)}^T$

Hence, $T=4$ years is the correct answer.