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RE: Poor Misunderstood Exponential Curve. It Gets Better

in #steemstem3 years ago (edited)

Well in a sense exponential growth is derived from assuming a linear (relation on the) rate of change. For example, consider the ODE dx/dt=x , the right-hand side is linear and its solution is given by x(t)= x(0)et. :)

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I was conscious when writing this that my own understanding of the math is not great. So the exponential curve I used here is a linear function because the rate of change is constant?

The rate of change of an exponential is not constant. But there is a linear relation between its derivative (=rate of change) and the actual function. Or more explicitely d(et)/dt=et , so when you take the derivative you get the same function back. Just like when you take the function y=x insert a number for x then the output, y, is equal to x. But in the case of the exponent the function in the previous example gets swapped with the derivative.

I think I should make it a project of mine to develop a good understanding of the basics of calculus. I have read a little bit about the history of its development, stretches over a really long period of human history. I have done a lot of statistics, but very weak in other areas. Thanks very much for the great explanation