Final answer:
Four half-lives have passed if a sample contains one-sixteenth of its original amount of radioactive material.
Step-by-step explanation:
Radioactive decay follows a predictable pattern wherein after each half-life, half of the remaining radioactive material decays.
Therefore, after the first half-life, half of the original sample remains. After the second half-life, one-quarter (half of the half) of the original sample remains, after the third half-life, one-eighth of the original sample remains, and after the fourth half-life, one-sixteenth of the original sample remains.
Consequently, if a sample has been reduced to one-sixteenth of its initial amount, this indicates that four half-lives have elapsed.