Half lives used carbon dating
As soon as a plant or animal dies, they cease the metabolic function of carbon uptake; there is no replenishment of radioactive carbon, only decay.
There is a useful diagrammatic representation of this process given here Libby, Anderson and Arnold (1949) were the first to measure the rate of this decay.
The reaction is: (Where n is a neutron and p is a proton).
The 14C formed is rapidly oxidised to 14CO2 and enters the earth's plant and animal lifeways through photosynthesis and the food chain.
Even though it decays into nitrogen, new carbon-14 is always being formed when cosmic rays hit atoms high in the atmosphere.
Plants and animals which utilise carbon in biological foodchains take up 14C during their lifetimes.
They exist in equilibrium with the C14 concentration of the atmosphere, that is, the numbers of C14 atoms and non-radioactive carbon atoms stays approximately the same over time.
They found that after 5568 years, half the C14 in the original sample will have decayed and after another 5568 years, half of that remaining material will have decayed, and so on (see figure 1 below).
The half-life () is the name given to this value which Libby measured at 556830 years. After 10 half-lives, there is a very small amount of radioactive carbon present in a sample.