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Well seems like I have a mathematical breakdown at the moment.. But I'm wondering, how CAN you actually solve a function of the form

$y = y_0 + Ae^{Bx} + Ce^{Dx}$ (Where B & D are negative, non zero numbers)

For x? If so how? (Will it become at least A BIT pretty?)

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up vote 2 down vote accepted

One thing you can do is let $z=e^x$. Then

$$y=y_0+A z^B + C z^D.$$

If you can solve that equation, then $x=\log{z}$.

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You will have to look for a numeric solution unless there is a special relationship between $B$ and $D$.

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