Assume a substance has a half-life of 19 years and the initial amount is 132 grams. How long will it be until only 35 % remains?

The answer to the question is

It will be ≅ 28.8 years until only 35 % of the substance remains

Explanation:

To solve this we note the required relations and the given variables thus

The half life of the substance is

N(t) = N(0) ×

Thus when only 35% is remaining we have

35% of N(0) = N(0)×

or 0.35 =   , to solve the previous equation, we take the log of both sides thus

Log (0.35) = Log ( ) or × log (1/2) =log(0.35)

⇒   = 1.515 and since = 19 years we have

t = 19 × 1.515 = 28.776 Years

Therefore it will be 28.776 years before 35 % of the substance will be remaining

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