This is a typical representation for age dating. We plot parent against daughter concentrations. In this hypothetical example there are no daughter atoms present in the original rock but a certain amount of parent atoms (so the composition plots on the parent axis). Consequently a line passing through this point to the origin has zero slope. After time a number of parent atoms have decayed (so total goes down) and the number of daughters increase. Eventually there will be no parents and only daughters - the composition will plot on the daughter axis. Note therefore the gradient of line connecting any composition with the origin increases with time. Or - the gradient of the line is a function of time. It is also a function of the decay constant.

In practice however, there are commonly daughter atoms already present in a material. In these cases we must make a correction, estimating the original daughter concentration. We can do this by normalising against a stable isotope of the daughter atom (argon 36 for the K-Ar system; strontium 86 for the Rb-Sr system).

Dating rocks