@maxdancona,
HEY MARK!! Just in case you pay attention to other people besides yourself, Radiometric dating ( having nothing to do with meet-upping) was discovered by a CHEMIST , so, as a trained geochemist and Economic geologist, I feel familiar with the coveys and corners about the technique than a mathematician who doesnt know chemistry--although I often do derive a lot of ordinary differential equations-( However I mostly use excel when I have to make excessively long model expansions)IS THAT OK??
You can sound a whole lot more informed about radiometric dating by reading K W Lee's
Geochronological Methods(in the AGI handbook), or Roger Wiens
Radiometric Dating from a Christian Perspective or Frank Steiger's
Radioactive Dating . I often used these as class guides for my intro students and , while they dont get into the machinery and lab methods involved, they are excellent mathematical explanations for majors (If youve gone through diff equations they're pretty strait forward and accessible.)
PS isotopes do disintegrate at varying rates within a fairly set range, so our uses of specific decay constants are actually longer term expansions of a simple dN/dt= (Lambda), where N is the number of isotopes we strt with per unit time in seconds(dt) and (Lambda) is the resultant decay constant. Decay constants are often rerun vry decae or so by longer times (t) and our decay constants do change by the 10th to the 11th decimal place if we need to be more accurate to the nearest BILLION years. SO I THINK WE MAY HAVE TAKEN ALL THAT INTO ACCOUNT, pretty Clever that Berty Boltwood eh?