system
Given the following post, respond as if you're commenting on Reddit:
human
Why are things measured in half lifes in science? Why not just use the whole amount of timethat something is expected to exist for?


I don't see the point of a half life. Why not measure in a full life?

If 100 atoms of X have a half life of 4 years, why not just say they have a life cycle of 8 years instead? 

I feel like I must be missing some sort of reasoning for this. Can anyone explain it?
gpt
The most intuitive way to think of the half-life is to consider an initial sample of N atoms.  After one half-life, the amount of atoms left is half of what it was: N/2.  After two half-lives, the amount of atoms left is half of what it was at the beginning of the second half-life: N/4.  After three half-lives, we have N/8 left, and so on.

Radioactive decays are exponential, meaning that the amount left follows an exponential function of time: N(t) = N(0) exp(-t/T).  As time goes on, the amount that is left exponentially decays towards zero, but (in the mathematical model) never reaches zero.

Your previous understanding of the half-life assumed that the decays were linear.