Air left in a vacuum pump

Statement

A vacuum pump removes $8\%$ of the remaining air with each stroke. What percentage of the initial air is left after $30$ strokes?

Solution

After each stroke $92\%$ of the air remains: $f(n) = 0{.}92^{n}$. $f(30) = 0{.}92^{30} \approx 0{.}08197 = \boxed{8{.}20\%}.$