How is exponential decay related to a half-life?

1 Answer
May 5, 2018

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

Explanation:

Assume you have an initial quantity (Q_0Q0) of a substance with a half-life period of hh, then after tt time periods the quantity remaining (Q_tQt) will be given by:

Q_t = Q_0*(1/2)^(t/h)Qt=Q0(12)th

This means that the quantity will halve in value after hh 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 786.1Q5=1000(12)514.4786.1 gm

Q_50 = 1000 *(1/2)^(50/14.4) approx 90.1Q50=1000(12)5014.490.1 gm

This is a form of exponential decay.