The rates of radioactive decay vary a lot. Some are expressed in milliseconds while others, like that of U-238, run into the billions of years. How can the half-life of such a long-lived isotope be determined?
Clearly no one can wait around for half of a
sample of U-238 to decay. And the changes in a sample even within
a human lifetime would be difficult to measure. Fortunately it is
not necessary to do so. Because the rate of decay is proportional to the amount of sample, a geiger counter (or more sensitive detector)
and the rate equation can be used to determine the half-life of
an isotope. 
A more typical use of the rate equation is to
determine the amount of sample that might remain at a given time
or to estimate how long it will take a sample to decay to a
certain amount.
