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If c-14 is constantly decaying, how is it that a living being had a constant amount of C-14 throughout its lifetime?

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All organic material has decaying Carbon-14 in it. But if plants and animals are still alive, they constantly replace the supply of Carbon in their systems so the amount of Carbon 14 in the system stays constant. Once a plant or animal dies, the Carbon is no longer regenerated and so the Carbon 14 starts to decay.

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