I do understand that radioisotope decay is modeled exponentially, and that a majority of this dating technique is centered in probability.
The margin for error, as I see it presently, cannot be small.
Current understanding of the history of life is probably close to the truth because it is based on repeated and careful testing and consideration of data.
The rejection of the validity of fossils and of dating by religious fundamentalists creates a problem for them: Fossil sequences were recognized and established in their broad outlines long before Charles Darwin had even thought of evolution.
This age is computed under the assumption that the parent substance (say, uranium) gradually decays to the daughter substance (say, lead), so the higher the ratio of lead to uranium, the older the rock must be.
Early geologists, in the 1700s and 1800s, noticed how fossils seemed to occur in sequences: certain assemblages of fossils were always found below other assemblages. Since 1859, paleontologists, or fossil experts, have searched the world for fossils.
In the past 150 years they have not found any fossils that Darwin would not have expected.
All ordinary matter is made up of combinations of chemical elements, each with its own atomic number, indicating the number of protons in the atomic nucleus.
Additionally, elements may exist in different isotopes, with each isotope of an element differing in the number of neutrons in the nucleus.