Integral Calculus, Radioactive Decay

Radioactive Decay

The exponential function is applicable whenever the change in a quantity is proportional to that quantity, and the change is happening all the time. This is the case with radioactive decay. Atoms decay with a certain probability, independent of the surrounding atoms, so the change in radioactive material is proportional to the amount of material.

Assume an atom of greenium becomes an atom of yellowium with 50% probability in one day. In other words, its half life is 24 hours. If you start with one pound of greenium, you'll have (1/2)^d pounds after d days. After 12 hours, or half a day, you'll have the square root of 1/2, or 0.707 pounds. You can calculate the amount of greenium for each second, or each millisecond, if you wish, using the exponential definition of (1/2)^d.