Radioactive isotope dating is fallible
So: The general approach to assessing gain or loss is to look at the isotope abundances in different minerals and see if there's a pattern.If the ratio is constant, we can be pretty sure there's been no gain or loss.
If the decay constant is very small, even tiny amounts of contamination by other radioactive materials can be very significant.Rubidium-strontium dating is more robust, and uranium-lead dating can survive fairly significant metamorphism without resetting.If a system gains or loses isotopes in a predictable way, it may be possible to estimate the loss and correct the age.So accurate determinations require very pure samples, very accurate and selective detectors, or both.The true age of a sample is self-explanatory, but unless the material dates from historic times, the true age is rarely known.Carbon-14 dating is often used for historical objects and young prehistoric objects, but it's based on the fact that all living things start out with a known amount of carbon-14. If the arrowhead is stuck in a bone, you can date the bone.
The most common dating methods for rocks are based on radioactive isotopes of potassium, rubidium, uranium, and thorium.
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!
If the rocks have an interbedded lava flow or volcanic ash bed, it's gold.
The older our sample is, the more daughter isotope it will contain relative to the parent.
But there are some questions that come to mind: Calculus students typically meet this problem somewhere in the second semester.