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

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(5328) (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.
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