Radioactive decay happens at a constant rate, which we can measure. Given a specific radioactive compound, we can precisely measure the quantity of its decay products and calculate from that how long the decay has been taking place. As long as there is still radioactive starting material, that length of time calculated is the age of the object being dated.
We express exponential relationships in terms of logarithms, all of which have a linear phase, which closely approximates the linear slope equation, y = ax + b. Within that linear portion of a logarithmic curve, radiometric dating methods are extremely accurate. The large errors only appear outside of the linear portion of the curve.
Such methods might provide mathematical precision, but fail to address the identification problem.