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#### RE: Poor Misunderstood Exponential Curve. It Gets Better

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)e^{t}. :)

flyyingkiwi (55)3 years agoI 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?

mathowl (64)3 years ago (edited)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(e

^{t})/dt=e^{t}, 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.flyyingkiwi (55)3 years agoI 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