Dating methods used on otzi
It's not that the radioactive carbon in air or food doesn't decay, it does.
Radiocarbon dating is used to work out the age of things that died up to 50,000 years ago. As far as working out the age of long-dead things goes, carbon has got a few things going for it. The proteins, carbohydrates and fats that make up much of our tissues are all based on carbon.
Everything from the fibres in the Shroud of Turin to Otzi the Iceman has had their birthday determined the carbon-14 way. There's plenty of hydrogen, oxygen and nitrogen in living things too, but carbon's got something none of them do — a radioactive isotope that can take thousands of years to decay.