Half-life of a substance

Statement

A radioactive substance decays by $12\%$ per year. After how many years is it reduced to half?

Solution

Each year $88\%$ remains: $0{.}88^{n} = 0{.}5$. $n = \frac{\ln 0{.}5}{\ln 0{.}88} = \frac{-0{.}693147}{-0{.}127833} \approx \boxed{5{.}42\ \text{years}}.$