Growth Rate
Simply, quadratic growth is growth where the rate of change changes at a constant (positive) rate. For example, if you add 3 the first time, then you add 3.5 the next time, and 4 the time after that, that is quadratic growth. In this case, you added 0.5 to your rate of change each time.
In continuous terms, this says that the second derivative is constant (the change of the change is constant); in discrete terms this says that the second finite difference is constant.
Quadratic growth is a special case of a convex function, and should not be confused with exponential growth, a better-known growth function. "Convex growth" means "increasing at an increasing rate" (the second derivative or second difference is positive), while quadratic growth means "increasing at a constantly increasing rate" (the second derivative is positive and constant), and exponential growth mean "increasing at a rate proportional to current value" (second derivative is proportional to current value, which is positive; this is because the first derivative is proportional to the current (positive) value, hence (taking derivatives) second derivative is proportional to first derivative, hence (proportional to proportional is proportional, second derivative is proportional to first derivative). That is, quadratic and exponential growth are both different special cases of convex growth.
Read more about this topic: Quadratic Growth
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