0
$\begingroup$

I've empiricaly produced this exponential equation to express a graphical representation :

y = \left(a^x + (bx)²\right) \left((1-10^{-x}) x\right)

I know the constants $a$ and $b$.

Now, i would like to extract the formula to be able to calculate x plots separatively.

How can i factor this equation to solve x ?

$ x = ?$

I didnt practice maths for so many years, i almost completely forgot all of the factorisation rules so im likely stucked...
Some help would be greatly appreciated.

EDIT :

I forgot to say that A and B values can be restricted to a range allowing to find an acceptable solution. For example, a = 1 and b = 10

You can view the representation result in this spreadsheet : https://docs.google.com/spreadsheet/ccc?key=0AiLgphtsXoERdDN2Y2RTeUlEa1FaNFdSM3dsT0I5V3c

  • 0
    Unfortunately, I do not have the specialized skills to produce a good formula.2012-01-14

1 Answers 1

1

That is too complicated to solve explicitly, but it may be possible to solve numerically, if there is a solution (assuming $a$ is positive, there may be some negative values of $y$ for which there is no real solution).

For example if $y=2$, $a=3$ and $b=4$ then $x \approx -0.403132$ and $x \approx 0.503299$ are solutions.

  • 0
    It looked to me as if $(0,0)$ was the minimum point on the curve, so I just found positive and negative $x$ which gave $y$ too high and then used bisection methods to find solutions: there are many others ways of doing it. An alternative (at least to start) would to draw the curve.2012-01-14