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The ratio of carbon-12 and carbon-14 are constant in a living organism.
However, no more carbon-14 is absorbed after the organism dies.
The rate of decay of carbon-14 is known so this can be used to estimate the age of the organism. When something dies its body stops taking in carbon.
Radiocarbon dating, or Carbon 14 dating, relies on processes of radioactive decay. From this point onwards the carbon in the body will begin to decay.
Carbon dating has the peculiar property that it works primarily on dead things.