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If a number of samples are analyzed and the results are shown to define a straight line within error, then a precise age is defined because this is only possible if each is a closed system and each has the same initial ratio and age.

The uncertainty in determining the slope is reduced because it is defined by many points.

The research included analyzing pictographs from numerous countries over a span of 15 years.

So, if you know the radioactive isotope found in a substance and the isotope's half-life, you can calculate the age of the substance. Well, a simple explanation is that it is the time required for a quantity to fall to half of its starting value.

So, you might say that the 'full-life' of a radioactive isotope ends when it has given off all of its radiation and reaches a point of being non-radioactive.

The methods work because radioactive elements are unstable, and they are always trying to move to a more stable state. This process by which an unstable atomic nucleus loses energy by releasing radiation is called radioactive decay.

The thing that makes this decay process so valuable for determining the age of an object is that each radioactive isotope decays at its own fixed rate, which is expressed in terms of its half-life.