# SOLUTION: a sample of radioactive material decayed to 33% of its original mass after 8 days. find the half life of the material.

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 Question 549637: a sample of radioactive material decayed to 33% of its original mass after 8 days. find the half life of the material.Answer by KMST(1874)   (Show Source): You can put this solution on YOUR website!The amount remaining, after time is a fraction of the initial amount , with being the half-life. (Note: There are many (equivalent) ways to express that relationship/function, but this is the one that seems to make more direct sense: the fraction is multiplied times itself as many times as half-lives have passed). So, taking logarithms of both sides For the problem, with 33% remaining, , and (in days) So, we can find (in days), by solving --> --> --> (rounded) So the half-life is 5 days.