Question #2ac43

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1 Answer
Stefan V.
Dec 3, 2014

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 #

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