Water left in a tank

Statement

A tank loses $6\%$ of the remaining water each day. What percentage of the initial water is left after $20$ days?

Solution

The remaining amounts form a geometric progression with ratio $q = 0{.}94$: $a_n = 0{.}94^{\,n}$. $a_{20} = 0{.}94^{20} \approx 0{.}29011 = \boxed{29{.}01\%}.$