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In the case of radiocarbon dating, the half-life of carbon 14 is 5,730 years.This half life is a relatively small number, which means that carbon 14 dating is not particularly helpful for very recent deaths and deaths more than 50,000 years ago.During the industrial revolution (1850 - present) increasing amounts of fossil fuels were combusted. Since the carbon in these fuels was ancient, it contained no radiocarbon.
The surplus "bomb" radiocarbon is just one of the effects human have had on the ratio of C. After 5,730 years, the amount of carbon 14 left in the body is half of the original amount.If the amount of carbon 14 is halved every 5,730 years, it will not take very long to reach an amount that is too small to analyze.However, atmospheric testing of nuclear weapons in the late 1950's and early 1960's greatly increased the amount of radiocarbon in the atmosphere, so the decay rate of 14 decays per minute more than doubled. Therefore, radiocarbon dates are calculated to a "pre-bomb" age of 1950 A. Material which died after 1950 has such high amounts of radiocarbon its age is reported as "percent modern (1950)" (example 180% modern).