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Algebra/math 30 Pure (log) decay1/2 life problem

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Expert: - 3/2/2010


Question
The problem states: A substance decays from 16g to 12.5g in 5 years. What is the half life of this substance.I used the formula N(t)=No(2)^t/h... h= 5 log(12.5)-log 16/log2 Half life =14.21928095 but I was told the answer is 14.039. I'm not sure where I went wrong.

Answer
The answer you were given is correct

12.5 = (16)2^-(5/h)

ln(12.5) = ln(16)-(5/h)ln(2)

hln(12.5) = hln(16) - 5ln(2)

hln(12.5)- hln(16)= - 5ln(2)

h(ln(12.5)- ln(16))= - 5ln(2)

h = - 5ln(2)/(ln(12.5)- ln(16))

h = 14.0392725


I don't see how you arrived at h = 5 log(12.5)-log 16/log2  

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