If all we have is one data point, the formula above doesn't help much more than the original formula.But if we have multiple data points -- multiple measurements of different samples say within a single igneous rock, then these should all lie on a straight line, whose slope m is simply related to the age of the specimen by the formula m = e; instead, this original ratio actually comes out as a result of the calculation!
In mathematical terms, radioactive decay is governed by a simple exponential formula, taught in many high school math classes: P is the amount after time t, and L is the decay constant for the radioactive isotope.This decay constant L can be expressed in terms of the half life T (the time it takes for one-half of the material to decay) as L = log(2) / T, where log(2) = 0.693147... In other words, if we know P, or even merely their ratio, we can solve the above equation for the time t.The following is a brief technical description of how scientists determine dates with radiometric schemes.This section may be omitted if readers do not wish to follow the math (although the math used here is nothing beyond what is typically taught in a good high-school math analysis class).Along this line, a kickstarter-funded firm known as Consumer Physics has designed a handheld, consumer-oriented optical spectrometer, which can be used to measure the molecular constituents of an item (food items, etc.) that you shine its built-in light upon.
This cannot be used for radiometric dating, but it does suggest advanced technology such as this is rapidly advancing and soon will be available to consumers.A related article on the age of the earth and geologic ages presented the current best known values for these dates: Ages.The figures shown in that article are based on radiometric dating.As mentioned above, the isochron dating method boils down to plotting multiple data points, after some calculation, on a graph, which, if the measurements and calculations are done properly, should lie on a straight line, or very nearly on a straight line.The slope of this line, after another simple calculation, then gives the age.Radiometric dating is rooted in the rates of radioactive decay of various isotopes, which rates have been measured carefully in numerous laboratories beginning in the early 20th century.