OpenStax College Physics for AP® Courses, Chapter 31, Problem 10 (Test Prep for AP® Courses)

This is College Physics Answers with Shaun Dychko. A radioactive sample has N atoms initially and after 3 half-lives, how many atoms remain? So here's the table showing the number of atoms based on the number of half-lives. So after 0 half-lives, which is to say you know the beginning— before any time has passed— there are N atoms we are told. Then after 1 half-life, there are half as many atoms so that's N divided by 2. After 2 half-lives, we take half of the amount we started this next period with so we started this from 1 half-life to 2— this period began with N over 2 atoms— half of which remain after this next half-life so there's N over 4 atoms left now. And then for the next half-life, we begin this period from 2 to 3 with N over 4 atoms which we then multiply by a half to get N over 8 after 3 half-lives. So the answer is (c).