Plants and animals naturally incorporate both the abundant C-12 isotope and the much rarer radiocarbon isotope into their tissues in about the same proportions as the two occur in the atmosphere during their lifetimes.When a creature dies, it ceases to consume more radiocarbon while the C-14 already in its body continues to decay back into nitrogen.The dating process is always designed to try to extract the carbon from a sample which is most representative of the original organism.
The Greeks consider the first Olympic Games as the beginning or 776 BC.
If either assumption is wrong carbon-14 dating doesn't work.
The first assumption is fairly reasonable, though some scientists have recently called into question whether or not nuclear decay rates were accelerated in the past (this might change the rate of carbon-14 decay).
It takes another 5,730 for half of the remainder to decay, and then another 5,730 for half of what's left then to decay and so on.
The period of time that it takes for half of a sample to decay is called a "half-life." Radiocarbon oxidizes (that is, it combines with oxygen) and enters the biosphere through natural processes like breathing and eating.