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This always confused me - people talk about an exponential explosion, but the rate of change of e^x is e^x, so there is no actual 'knee' in the curve with a huge speedup afterwards...


or, if you prefer, every point is a 'knee' in the curve with a huge speedup afterward


Except in reality, when samples are infrequent and there is significant 'noise' in the data, it can be far from clear what shape the graph is. This is usually particularly true in the early stages of the development of a trend. How do you know you're in the early stages? You don't, but it's a big mistake to think that trends which eventually turn out to be exponential must therefore be obviously so at all times.




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