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Measuring the difference in the ratio between carbon-12 and carbon-14 is useful for dating the age of organic matter since a living organism is exchanging carbon and maintaining a certain ratio of isotopes.
In a diseased organism, there is no exchange of carbon, but the carbon-14 that is present undergoes radioactive decay, so over time, the isotope ratio becomes more and more different.
Volcanoes spew out CO which could just as effectively decrease the ratio.
So, if we find the remains of a dead creature whose C-12 to C-14 ratio is half of what it's supposed to be (that is, one C-14 atom for every two trillion C-12 atoms instead of one in every trillion) we can assume the creature has been dead for about 5,730 years (since half of the radiocarbon is missing, it takes about 5,730 years for half of it to decay back into nitrogen).
If the ratio is a quarter of what it should be (one in every four trillion) we can assume the creature has been dead for 11,460 year (two half-lives).
This is how carbon dating works: Carbon is a naturally abundant element found in the atmosphere, in the earth, in the oceans, and in every living creature.
C-12 is by far the most common isotope, while only about one in a trillion carbon atoms is C-14.