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I want to be able to manipulate the point of inflection of an exponential curve equation:$$a\exp\{xb\}.$$ could somebody tell me which parameter I may introduce in such a formula in order to make the resultant curve more bent, without changing anything else?

This pic represents what I want to do with the curve

Em.
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Agus camacho
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  • Desmos is nice for playing with coefficients: https://www.desmos.com/calculator/jrbmek3mae – Carser Feb 20 '16 at 00:36
  • The "knee" you wan to move would not be called a "point of inflection" by mathematicians. They use that term to refer to a place where curvature changes sign. – bubba Feb 20 '16 at 01:09
  • Excel lets you play with parameters in curve fitting. Look at the "Trend Line" function. – bubba Feb 20 '16 at 01:10
  • I already tried in excell and could not do what I want. By using desmos, it looks like what I want to do is not possible with an exponential function, but I should use another function. – Agus camacho Feb 20 '16 at 15:12

1 Answers1

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You can multiply your exponential with a second degree polynomial, $x^2$: $$f(x)=x^2ae^{bx+c}$$

You can then fiddle with $c$ to slide the whole graph left again. For example, open this Desmos-link in two different tabs and leave one of them as is. Then multiply the function in the other by $x^2$ and change $c$ to around $-5.7$. Now change between the two tabs to see the change.

Bobson Dugnutt
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