(For brevity's sake, hereafter I will refer to the parent isotope as ).
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.
Radiometric dating remains a reliable scientific method.
For articles on the RATE project, see the Rate Index.
Note that the mere existence of these assumptions do not render the simpler dating methods entirely useless.
In many cases, there are independent cues (such as geologic setting or the chemistry of the specimen) which can suggest that such assumptions are entirely reasonable.
New discoveries have filled in the gaps, and shown us in unimaginable detail the shape of the great ‘tree of life’.
Darwin and his contemporaries could never have imagined the improvements in resolution of stratigraphy that have come since 1859, nor guessed what fossils were to be found in the southern continents, nor predicted the huge increase in the number of amateur and professional paleontologists worldwide.
However, the methods must be used with care -- and one should be cautious about investing much confidence in the resulting age...
especially in absence of cross-checks by different methods, or if presented without sufficient information to judge the context in which it was obtained.
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.