Question

How is exponential decay related to a half-life?

Answer 1

Half-life is a form of exponential decay over time.
See below.

Explanation:

Assume you have an initial quantity (`Q_0`) of a substance with a half-life period of `h`, then after `t` time periods the quantity remaining (`Q_t`) will be given by:

`Q_t = Q_0*(1/2)^(t/h)`

This means that the quantity will halve in value after `h` time periods.

An example:

The half-life of Plutonium-241 is 14.4 years. If I start with 1000 gm after 5 years and 50 years I will have:

`Q_5 = 1000 * (1/2)^(5/14.4) approx 786.1` gm

`Q_50 = 1000 *(1/2)^(50/14.4) approx 90.1` gm

This is a form of exponential decay.