Radiometric dating parent daughter isotopes
We could be sure that a mineral containing parentium originally had no daughterium.
If the mineral contained 1 part per million Parentium-123 and 3 parts per million Daughterium-123, we could be sure all the Daughterium-123 was originally Parentium-123.
In particular, quartzites and carbonate rocks almost always don't have enough to permit dating.
What radioactive materials actually do is decay according to a law: Decays/Time = K * Number of atoms K is a constant called the decay constant.
Let t stand for time and N(t) stand for the number of atoms at time t .
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.
If only there were long-lived isotopes of silicon, calcium, and magnesium!
But there are some questions that come to mind: Calculus students typically meet this problem somewhere in the second semester.