This function represents exponential decay.
It is only an approximate solution, for two reasons. Firstly, the exponential function is continuous, but the physical quantity N can only take positive integer values. Secondly, because it describes a random process,
it is only statistically true. However, in most common cases, N is a very large number and the function
is a good approximation.
In addition to the decay constant, radioactive decay is sometimes characterized by the mean lifetime. Each atom "lives" for a finite amount of time before it decays, and the mean lifetime is the arithmetic mean of all the atoms' lifetimes. It is represented by the symbol τ, and is related to the decay constant as follows:
http://en.wikipedia.org/wiki/Radioactiv ... cay_timing