Anthropologists can estimate the age of a bone or other sample of organic matter

Question

Anthropologists can estimate the age of a bone or other sample of organic matter by its carbon-14 content. The carbon-14 in a living organism is constant until the organism dies, after which carbon-14 decayss with first order kinetics and a half life of 5730 years. Suppose a bone from an ancient human contains 19.5%of the C-14 found in living organisms. How old is the bone?

If you could explain your steps with words (especially explaining the math and what the variables mean) that would be super helpful! Thank you!

Explanation / Answer

ln([A] / [Ao]) = -kt First, find k from the known half-life: ln(1/2) = -k (5730yrs) k = 1.21x10^-4 Now use k in the same equation to find the time for 21%: ln(21/100) = -1.21x10^-4 * (t) -1.561 = -1.21x10^-4 * (t) t = 12,900 yrs

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