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 #
