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January 17th, 2017, 05:10 PM  #1 
Newbie Joined: Jan 2017 From: Warrington Posts: 2 Thanks: 0  Exponential Decay
The equation for exponential decay is N = N0 e^(at) where N is the population at time t and N0 the amount at time t = 0. Find the age t , if an initial population of 14C atoms has decayed to 0.1% of its original amount and the decay parameter a is 1.226 × 104 y1. Any suggestions/agreement on the answer to this question. Please note that the 'a' is supposed to be an alpha symbol, although an 'a' does the same job. I have an answer of 56344 years, although I'm doubting this answer as this just about on the borderline of the maximum age for carbon dating. Thanks in advance. 
January 17th, 2017, 05:23 PM  #2 
Math Team Joined: Jul 2011 From: Texas Posts: 2,815 Thanks: 1458 
works fine for me ... if they really detected a 0.1% carbon 14 level $N = N_0 e^{at}$ 100% of $C_{14}$ at $t = 0$ $0.1 = 100 e^{at}$ $0.001 = e^{at}$ $\ln(0.001) = at$ $t = \dfrac{\ln(0.001)}{a} = \dfrac{\ln(0.001)}{1.226 \times 10^{4}} = 56344$ years 

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