How do geologists determine the absolute ages of rocks with radioactive decay?

Imagine you have a whole pie to yourself. The first day you eat half the pie, and save the other half for later. The second day you eat half of what's left (leaving 1/4 of the original pie). The third day you eat half again of what's left (leaving 1/8th), and so on until you finish the pie (or get sick of it). If your mom walked in and saw 1/16th of a pie (and knew that you had been eating half of what was left every day), she could quickly determine that the pie was four days old.

Radioactive decay works the same way. Some elements (uranium, for example) are unstable, and decay to a different element (uranium to lead, for example). The good news is that the decay rate from parent element to daughter element is constant (we assume), and is called the "half-life" (clever name, huh?).

So, when geologist find one of the unstable elements in a rock, all they have to do is measure how much of the parent element remains, how much of the daughter element has been formed, apply the half-life value, and do the math. Pretty simple, actually.