A mathematical explanation of carbon dating and half life
Isotopic systems that have been exploited for radiometric dating have half-lives ranging from only about 10 years (e.g., tritium) to over 100 billion years (e.g., samarium-147).For most radioactive nuclides, the half-life depends solely on nuclear properties and is essentially a constant.
However, the principle of carbon-14 dating applies to other isotopes as well.
For all other nuclides, the proportion of the original nuclide to its decay products changes in a predictable way as the original nuclide decays over time.
This predictability allows the relative abundances of related nuclides to be used as a clock to measure the time from the incorporation of the original nuclides into a material to the present.
Radio carbon dating determines the age of ancient objects by means of measuring the amount of carbon-14 there is left in an object.
A man called Willard F Libby pioneered it at the University of Chicago in the 50's. This is now the most widely used method of age estimation in the field of archaeology.