Since radioactive decay is a spontaneous process, it is impossible to predict when a radioisotope will decay. It is more convenient to describe the amount of time needed for a certain quantity to decay. The quantity chosen is one half the original amount. Thus, the half-life [local] of a radioisotope is the amount of time required for one half of the original quantity to decay.

Radioactive decay is spontaneous and is described as a continuous exponential function.

Where the amount of undecayed radioisotope (A) is a function of the starting amount (A_o), the decay constant (k), and the time. The decay constant is different for each radioisotope and can be described as a function of the half life. Solving for k at half life conditions and applying that value to the above equation gives an equation that describes the amount of undecayed radioisotope at any time as a function of the half life (t*).