When an unstable nucleus "decays" it does so with a particular rate that is characteristic of that nucleus and the amount of sample present. The fact that the rate depends on the amount of sample present means that it is following first order kinetics. We can represent the rate in equation form as:

rate = k N

where the rate is measured at a given time, t, k is the rate constant for that particular isotope, and N is the amount of sample present (or some quantity proportional to the amount of sample). As with any chemical rate, these rates change over time as less reactant remains. There is an alternative way to represent the rate of a reaction which takes this into account (and resorts to calculus to do it):