Years for the population to exceed a threshold

Statement

A population grows by $3\%$ each year starting from $50000$ inhabitants. After how many years will it exceed $80000$?

Solution

$50000\,(1{.}03)^{n}>80000\Rightarrow (1{.}03)^{n}>1{.}6$. $n>\frac{\ln 1{.}6}{\ln 1{.}03}=\frac{0{.}470004}{0{.}029559}\approx 15{.}90\Rightarrow\boxed{n=16\ \text{years}}.$