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Homework Statement
Nitrogen in the upper atmostphere is convereted by radiation to carbon 14
the halflife of carbon, [tex] \tau = 5730 [/tex] years
carbon 14 makes up a known proportion of living plants and animals, after they die, the proportion of carbon 14 decays.

History records that an eruption on Mount Vesuvius buried the city Pompeli in 79 AD
excavations uncovered bones and these contain 79.17 % of the original carbon 14:
the question:
Does the radiocarbon dating agree with the historical record?

The Attempt at a Solution
I'm going to assume that the percentage of undecayed mass, 79.17% was measured in 2010
as the question dosen't say when
2010  79 = 1931, the number of years passed
[tex] \frac{1931}{\tau} [/tex] = [tex] \frac{1931}{5730} [/tex] = 0.3369 % [tex] \tau [/tex]
now that means it should be 100%  33.69% of the original mass
= 0.663%,
So i'm going to say that the radiocarbon dating dosen't agree with the historical record, and that the bones uncovered had been of people that had died before the eruption on Vesuvius,

Can someone confirm that i've done this correctly?
thanks