Exponential Behavior draft V0.1
The explanation starts with a discussion of the well known story of the grains of wheat and the chess board.
Exponential patterns are common in natural systems, but the implication of exponential growth and decay can be hard to comprehend.
My favorite illustration of this is the story of the wheat and the chessboard.
There are many variations of the story, but the basic idea is that a wise man once asked a king to reward him by giving him as much wheat as could fit on a chess board based on the following pattern:
Place one grain of wheat on the first square,
two on the second,
four on the third,
and continue doubling the number of grains until the entire board is full.
Most people's intuition is that this won't add up to very much wheat.
That was the king's reaction, but after agreeing, he discovered that the 64th square of the board requires an astoundingly large 9.2×1018 grains of wheat.
The reason these questions trick us is that this is an exponential relationship and we don't have an intuitive sense of exponential patterns.
We see these small increases at the start of the set and fail to appreciate how quickly this continued doubling creates large numbers.
Continue into discussion of exponential patterns and where they are found in natural systems
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I like how this has started, but I need to take some time to figure out how to proceed from here.