The rate of decay of radioactive material is measured by the lifetime . If we start with atoms at time , the number of atoms remaining after time is given by

 (1)

The halflife is the time it takes for half of the atoms to decay. It is easily found from the above formula:
 (2)

Over an interval of time , the number of atoms decreases. The decrease is given by the negative number
 (3)

The number of decays in this interval is the postive number
 (4)

So
 (5)

is called the decay rate. It gives the number of decays per unit time at any instant in time.