Through analysis, a bone fragment is determined to contain 13% of its original carbon-14.

The half-life of carbon-14 is approximately 5,730 years. Since the quantity represents 13% (or 13/100ths) of , it follows that Thus the bone is approximately 17,000 years old.

As long as an organism is alive, the amount of C-14 in its cellular structure remains constant.

But when the organism dies, the amount of C-14 begins to decrease.

Although the time at which any individual atom will decay cannot be forecast, the time in which any given percentage of a sample will decay can be calculated to varying degrees of accuracy.

The time that it takes for half of a sample to decay is known as the half life of the isotope.

Scientists know the half-life of C-14 (5,730 years), so they can figure out how long ago the organism died.

Knowing about half-lives is important because it enables you to determine when a sample of radioactive material is safe to handle.It might take a millisecond, or it might take a century. But if you have a large enough sample, a pattern begins to emerge.It takes a certain amount of time for half the atoms in a sample to decay.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 meaning of this equation is that the rate of change of the number of nuclei over time is proportional only to the number of nuclei.