# Math-Exponential Decay

A lab technician had 58 grams of a radioactive substance. Ten days later, only 52 grams remained. Find the half-life of the radioactive substance.

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1. if the half-life is n days, then the amount remaining after t days can be modeled by

58(1/2)^(t/n)

So, to find n, we just have to solve

58(1/2)^(10/n) = 52
(1/2)^(10/n) = 52/58 = 0.8966
10/n = log(52/58)/log(1/2)
10/n = 0.1575
n = 63.5

So, the half-life is about 63.5 days

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posted by Steve

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