Carbon-14 dating has an interesting limitation in that the ratio of regular carbon to carbon-14 in the air is not constant and therefore any date must be calibrated using dendrochronology.
The half-life , specific to each nuclide, can be accurately measured on a pure sample, and is known to be independent of the chemical composition of the sample, temperature and pressure.
You find a bone fragment and through analysis you determine that it contains 13% of its original carbon-14.
Given isotopes are useful for dating over a range from a fraction of their half life to about four or five times their half life.
Symbolically, the process of radioactive decay can be expressed by the following differential equation, where N is the quantity of decaying nuclei and k is a positive number called the exponential decay constant.
The time that it takes for half of a sample to decay is known as the half life of the isotope.