Assume the substance has a half-life of 11 years and the initial amount is 126 grams. how long will it be until only 15 % remains?

(126) times (1/2 to the x/11 power) = 15% times 126

(1/2) to the x/11 power = 0.15

Take the log of both sides :

(x/11) times log(1/2) = log(0.15)

Multiply both sides by 11 :

'x' times log(1/2) = 11 x log(0.15)

Divide both sides by " log(1/2) " :

x = 11 x log(0.15)/log(1/2) = 30.107 years (rounded)

That's the time it takes for any-size sample of this substance
to decay to 15% of its original size.

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