I believe the answer is 108 hours.
An exponential decay process can be described by the following equation:
N(t) = N_0(t) * (!/2)^(t/t_(1/2)) , where
N(t) - the initial quantity of the substance that will decay;
N_0(t) - the quantity that still remains and has not yet decayed after a time t;
t_(1/2) - the half-life of the decaying quantity;
This being said, we know that our t_(1/2) is equal to 21.6 hours, our N(t) is 11.25 grams, and our N_0(t) is equal to 360 grams.
Therefore,
11.25 = 360 *(1/2)^(t/21.6) . Now, let's say t/21.6 is equal to y.
We then have
11.25/360 = (1/2)^y
So y = log_(1/2)(0.03125) = 5
Replacing this into
t/21.6 = 5 we get t = 108 hours
