We will deal with carbon dating first and then with the other dating methods.Carbon has unique properties that are essential for life on Earth.
The radioactive isotope carbon-14 is created in the upper atmosphere when cosmic-ray particles from outer space strike nitrogen atoms and transform them into radioactive carbon.
Some of the carbon-14 might find its way into living creatures.
An example of the ingenious technical work and hard-fought debates underlying the main story is the use of radioactive carbon-14 to assign dates to the distant past.
For other examples, see the essays on Temperatures from Fossil Shells and Arakawa's Computation Device.
Once an organism is decoupled from these cycles (i.e., death), then the carbon-14 decays until essentially gone.
The half-life of a radioactive isotope (usually denoted by \(t_\)) is a more familiar concept than \(k\) for radioactivity, so although Equation \(\ref\) is expressed in terms of \(k\), it is more usual to quote the value of \(t_\).
After a creature's death the isotope would slowly decay away over millennia at a fixed rate.
Thus the less of it that remained in an object, in proportion to normal carbon, the older the object was.
Clearly, such huge time periods cannot be fitted into the Bible without compromising what the Bible says about the goodness of God and the origin of sin, death and suffering—the reason Jesus came into the world (See Six Days? He said, This only makes sense with a time-line beginning with the creation week thousands of years ago.