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On The Double II
How do we calculate doubling times from growth rates?
A doubling time is the amount of time, assuming constant growth, it takes for a quantity to double. Researchers often calculate this figure for population growth in cells, animals, and humans.
How should we think about exponential growth? Exponential growth means something increases in relation to its current value. Imagine you covered the squares of a 64-square chess board with game pieces. Each step doubles the number of filled squares. After four rounds, eight squares have a piece. Three generations later, pieces fill the whole board.
It does not mean ‘fast’ — savings accounts with low interest rates have this kind of growth. One way is to describe the changing volume with a simple mathematical model. Here, there is a constant, representing volumes at the start. We multiply that constant factor by a base number, raised to the power of a fixed growth rate multiplied by time.
For positive whole numbers, exponentiation is the act of repeated multiplication. ‘Two to the power of three’ is the same as two times two times two. The natural base for this exponentiation process is Euler’s number, which is about 2.718. That number has many special properties. Its exponentiation function is equal to its own derivative.
