Question

The population of a city increases at the rate of $2$% per year. How many years will it take to double the population?

Answer 1

Given,

Let "x" be the inintial population and "2x" be the final population.

$x(1+2$ % ${)}^n=2x$

${(1+\frac{2}{100})}^2=2$

${\left(\frac{102}{100}\right)}^n=2$

${\left(\frac{51}{50}\right)}^n=2$

taking log on both sides, we get,

$n=\frac{\log 2}{\log \left(\frac{51}{50}\right)}$

$\therefore n=35$

Thus, in 35 years the population doubles.