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Colloquial sense:

It's when the rate of growth is always increasing, rather than the rate of growth being constant.

Mathematical sense (a more exact definition):

It's when the rate of increase is directly proportional to the amount. This means that the amount will be multiplied by the same number over fixed periods of time.

For example, if you have ten thousand dollars in a bank account with a fixed interest rate (exponential growth) and the amount is currently increasing at a rate of one dollar per day, then when the money grows to fifteen thousand dollars it will be increasing at $1.50 per day. If your money takes ten years to triple from $200 to $600 then it will take another ten years for it to triple again to $1800.

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