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| Math Central | Quandaries & Queries |
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Question from Malachi, a student: I am doing carbon 14 dating and i figured out the rule for taking the percent of the original C-14 to figure out how old it is. how do I work the equation the other way around to find the percent remaining, from how long ago the objects organic mater died |
Malachi,
From your previous question I know you are looking at
http://mathcentral.uregina.ca/beyond/articles/ExpDecay/Carbon14.html.
The formula in this document is 
. To solve for N first multiply both sides by -0.693 and then divide each side by t1/2. The result is
-0.693 t/t1/2 = ln(N/N0).
To simplify the notation let K = -0.693 t/t1/2 so that the equation becomes
K = ln(N/N0).
Now apply the exponential function to each side and you have
eK= N/N0
or
N = N0 eK.
Harley
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