Differential equation for carbon dating

Carbon is naturally in all living organisms and is replenished in the tissues by eating other organisms or by breathing air that contains carbon.At any particular time all living organisms have approximately the same ratio of carbon 12 to carbon 14 in their tissues.Where t is the age of the fossil (or the date of death) and ln() is the natural logarithm function.When finding the age of an organic organism we need to consider the half-life of carbon 14 as well as the rate of decay, which is –0.693.

Archaeologists use the exponential, radioactive decay of carbon 14 to estimate the death dates of organic material.The stable form of carbon is carbon 12 and the radioactive isotope carbon 14 decays over time into carbon 12 and other particles.

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