Exponential growth, the coin game
Apart from coins this game can be played with cards, dice and in fact anything for which individual faces can be observed.
Lay a sheet out on the ground and place a coin in it. Then repeatedly
- Gather up the sheet with plenty of air in it, shake it and set it back down
- Spread out the coins into a single layer
- For every coin that landed heads up add two more coins to the sheet
You may want to keep track of the number of coins in the sheet before each shake so that you can plot, say, a column chart like the one above. It is expected that half the coins will be heads up so, on average, the number of coins in the sheet will double after each shake. i.e. Exponential growth.
The flipping of a coin is called a Bernoulli trial and each shake is seen to result in the drawing of a sample from the resulting Binomial distribution. For a large number of coins the Binomial distribution can be approximated by a Normal distribution and the resulting noisy growth is known as Geometric Brownian Motion.