The sample from the human remains is approximately
12,820 years old
Given the model used for radiocarbon dating after a particular period of time "t" expressed according to the formula;
[tex]Q(t)=b_0e^{-0.0001211t}[/tex]
If a sample from a human bone taken from the site showed that 21.2
% of the carbon-14 still remained, then Q(t) = 21.2
Substitute the given parameters into the formula:
[tex]Q(t)=b_0e^{-0.0001211t}\\0.212b_0=b_0e^{-0.0001211t}\\0.212 = e^{-0.0001211t}\\ln0.212=lne^{-0.0001211t}\\-1.55117=-0.0001211t\\t=\frac{1.55117}{0.000121}\\t= 12,819.56 years[/tex]
Hence the sample from the human remains is approximately
12,820 years old
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