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.