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However, unlike in an exponential decay, the half-life depends on the initial quantity, and the prospective half-life will change over time as the quantity decays.As an example, the radioactive decay of carbon-14 is exponential with a half-life of 5,730 years.For example, the medical sciences refer to the biological half-life of drugs and other chemicals in the human body. The original term, half-life period, dating to Ernest Rutherford's discovery of the principle in 1907, was shortened to half-life in the early 1950s.Rutherford applied the principle of a radioactive element's half-life to studies of age determination of rocks by measuring the decay period of radium to lead-206.Nevertheless, when there are many identical atoms decaying (right boxes), the law of large numbers suggests that it is a very good approximation to say that half of the atoms remain after one half-life.
Thus, the mixture taken as a whole will not decay by halves.Note the consequence of the law of large numbers: with more atoms, the overall decay is more regular and more predictable.A half-life usually describes the decay of discrete entities, such as radioactive atoms.The decay of many physical quantities is not exponential—for example, the evaporation of water from a puddle, or (often) the chemical reaction of a molecule.In such cases, the half-life is defined the same way as before: as the time elapsed before half of the original quantity has decayed.
For example, the image on the right is a simulation of many identical atoms undergoing radioactive decay.