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Not only that, we top up our carbon-14 levels every time we eat.
And plants top up their radioactive carbon every time they turn carbon dioxide to food during photosynthesis.
That age range is then compared with known 14C/12C ratios from the tree ring/marine record to find the best match, and the result is a calibrated age range you can be 95 per cent sure of.
By about 58,000 years (ten half-lives) after an organism has died, there's so little radioactive carbon left (less than 1/1000) that calculations of age are no longer accurate.