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In calculus terms, we write: d N(t)/dt = -K * N(t) or d N(t)/N(t) = -K dt The minus sign means that each decay decreases the total number of atoms.Integrating both sides, we get: ln N(t) = -Kt C C is the constant of integration that we can often ignore, but not here.Sedimentary rocks are generally hard to date because common cements like silica don't have datable radioisotopes, and minerals like glauconite that are common in sedimentary rocks are very prone to resetting.
Weathering and metamorphism are the two most common ways to disturb a system.Imagine we have an undiscovered element, Parentium, that has a radioactive isotope, Parentium-123, which decays to stable Daughterium-123.This is the only way Parentium-123 decays, and there is no other source of Daughterium-123.Suppose, in repaving your driveway, you find a stash of old coins buried in the ground. Of course there are more outlandish explanations, like somebody counterfeiting 1920 coins in 1900 (and successfully anticipating any changes in design in the meantime), or secretly tearing up part of the driveway after 1950, but unless someone comes up with really persuasive evidence, we're justified in ignoring these hypotheses.The driveway was poured in 1950, and the coins are all dated 1920. Radiometric dating generally requires that a system be closed - in other words, has not had material added or removed.