All animals in the food chain, including carnivores, get their carbon indirectly from plant material, even if it is by eating animals which themselves eat plants.The net effect of this is that all living organisms have the same radiocarbon to stable carbon ratio as the atmosphere.
Carbon 14 dating is not great for dating things like a year old because if much less than 1 half-life has passed, barely any of the carbon 14 has decayed, and it is difficult to measure the difference in rates and know with certainty the time involved.
On the other hand, if tons of half-lives have passed, there is almost none of the sample carbon 14 left, and it is really hard to measure accurately how much is left.
And given the fact that the ratio of carbon 14 to carbon 12 in living organisms is approximately 1 : 1.35x10 In actually measuring these quantities, we take advantage of the fact that the rate of decay (how many radioactive emissions occur per unit time) is dependent on how many atoms there are in a sample (this criteria leads to an exponential decay rate).
We have devices to measure the radioactivity of a sample, and the ratio described above translates into a rate of 15.6 decays/min per gram of carbon in a living sample.
For radiocarbon dating to be possible, the material must once have been part of a living organism.
This means that things like stone, metal and pottery cannot usually be directly dated by this means unless there is some organic material embedded or left as a residue.
Once an organism dies the carbon is no longer replaced.
Because the radiocarbon is radioactive, it will slowly decay away.
So in the real world, looking at a sample like say a bone dug up by an archaeologist, how do we know how much carbon 14 we started with? This process is constantly occurring, and has been for a very long time, so there is a fairly constant ratio of carbon 14 atoms to carbon 12 atoms in the atmosphere.
Now living plants 'breathe' CO indiscriminately (they don't care about isotopes one way or the other), and so (while they are living) they have the same ratio of carbon 14 in them as the atmosphere.
If it weren’t for the amiability of carbon, simple organic matter couldn’t have evolved to achieve the extraordinary, inscrutable complexity it now boasts: the complexity to develop a system to sense, to breathe, to digest, to excrete and in a lean, hairless primate, even a system to think.