Question

What percentage of a radioactive species would be found as daughter material after five half-lives?

Answer 1

The equation for half-life is

AT = A0 2 (-T / H)

where A0 is the starting activity, AT is the activity at some time T, and H is half-life in units of T.

As a result, seven half-lives would be 2(-7) or 0.0078125 of the original activity.

Answer 2

Or, because you are working with whole numbers of half lifes just divide 100% five times.\[\color{green}{100\% \rightarrow 50\% \rightarrow 25\% \rightarrow etc.}\]
That will give you the precentage of the original sample decayed. Think about what else you will have to do to find out the percentage of the daughter nuclei formed.