let me help you out here... http://www.howstuffworks.com/carbon-14.htm
They do a good job of explaining the 1/2 life period, however, they fail to address the one crucial element that is rooted in the scientific method. Observation. Starting with Carbon 14, who has observed Carbon 14 decaying to 1/2 of its original component 5,730 years ago? How about Thorium 232 and 14 billion years?