What is the relationship between radioactivity and half life

In Physics, there is an inverse exponential relationship between the half-life and the radioactivity of a substance. Half-life denotes the period during which a specific substance will decrease by 1/2 through radioactive decay. It can also be described as the period during which a single radioactive atom has a 1/2 probability of decaying some time during that specific duration. The shorter the half-life, the more radioactive that substance is. For example, a radioactive substance 'A' with a half-life of 5 days will decay twice as quickly as substance 'B' with a half-life of 10 days. Radioactive decay is a form of exponential decay. In the example above. If you started out with 100g of substance 'A' (half-life of 5 days) and 100 g of substance 'B' (half-life 10 days), then after 10 days, you would have 50g of substance 'B', and only 25g of substance 'A'. Note that, in life sciences, the term 'half-life' is a pharmacalogical term, and has nothing to do with radioactive decay.