Special classes of semigroups

When calculating the unstable fraction of the radioactivity in the original isotope nucleus, there is a simple equation which can help you find the fraction of unstable nuclei still radioactive after a given period of half-lives.

Equation

$p=1/2^n$

when $p$ is the fraction of unstable nucleus, and $n$ the number of half lives.

Example:

Q: The Half Life of Cobalt-60 is 5 years. After 225 years, what fraction of the Cobalt-60 is still unstable?

A: (225÷5=45 will find you the number of half lives.)

$p=1/2^n$

$p=1/2^{45}$