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January 17th, 2017, 05:10 PM   #1
Joined: Jan 2017
From: Warrington

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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 × 10-4 y-1.

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.
sgjaskey1 is offline  
January 17th, 2017, 05:23 PM   #2
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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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