The Dice Extinction Experiment
Roll a hundred dice, remove every six, and watch a population go extinct — a physical model of exponential decay you can hold in your hands.
Where this idea comes from
Start here — this is the source that inspired this exploration.
Introduction
Roll 100 dice on mathigon.org (or with real dice). Remove every die that shows a six, then re-roll what's left, and repeat until none remain. Each round removes roughly a sixth of what's left — the same shape as a population dying off, a radioactive sample decaying, or a drug clearing your bloodstream. Record how many dice survive each round and you have your own exponential decay data set, generated from something as ordinary as a dice roll. The real test is whether that same mathematical pattern survives contact with messier real data: where does a real medicine's concentration in the blood stop obeying a clean exponential curve?
Guiding Questions
- Take a geometric sequence with ratio less than 1 and the function y = a·b^x. How are they the same thing?
- Find real decay data — medicine in the bloodstream, cooling, radioactivity. Fit an exponential model.
- What is the half-life in your model, and how do you calculate it from the base b?
- Where does the exponential model stop matching your data, and what might explain that?