Exponential Decay

Jan 2017
2
0
Warrington
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. :)
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skeeter

Math Team
Jul 2011
3,206
1,731
Texas
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