Imagine we have an undiscovered element, Parentium, that has a radioactive isotope, Parentium-123, which decays to stable Daughterium-123.

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.

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 you don't have **minerals** with those elements, you can't date the rock.

In particular, quartzites and carbonate rocks almost always don't have enough to permit **dating**.

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.

When t = 0, ln N(0) = C Taking exponentials of both sides, we get N(t) = N(0)exp(-Kt) If t = one half life, then N(t)/N(0) = 1/2 = exp(-Kt), and: ln(1/2) = -ln2 = -Kt, so t = ln2 / K So *what* we do in practice is determine the decay constant and calculate half life from it.

If the decay constant is very small, even tiny amounts of contamination by other radioactive materials can be very significant.

But there are some questions that come to mind: Calculus students typically meet this problem somewhere in the second semester.