After plants die or are consumed by other organisms, the incorporation of all carbon isotopes, including 14C, stops.
Thereafter, the concentration (fraction) of 14C declines at a fixed exponential rate due to the radioactive decay of 14C. ) Comparing the remaining 14C fraction of a sample to that expected from atmospheric 14C allows us to estimate the age of the sample.
Above is a graph that illustrates the relationship between how much Carbon 14 is left in a sample and how old it is.The carbon-14 decays with its half-life of 5,700 years, while the amount of carbon-12 remains constant in the sample.By looking at the ratio of carbon-12 to carbon-14 in the sample and comparing it to the ratio in a living organism, it is possible to determine the age of a formerly living thing fairly precisely. So, if you had a fossil that had 10 percent carbon-14 compared to a living sample, then that fossil would be: t = [ ln (0.10) / (-0.693) ] x 5,700 years t = [ (-2.303) / (-0.693) ] x 5,700 years t = [ 3.323 ] x 5,700 years Because the half-life of carbon-14 is 5,700 years, it is only reliable for dating objects up to about 60,000 years old.This rather complex formula shows you how to solve this puzzle using accepted scientific methods. Carbon-14 dating can be used on objects ranging from a few hundred years old to 50,000 years old.