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I'm working on a pricing algorithm for work and I've reached a point where the rust on my brain is blocking the creative juices. I did a maths degree years ago, obviously deserving the odd fails I recorded, as I can't remember the rules for expanding exponents to determine whether this equation is solvable.

Suppose we have the following equation:

$y = pb^{c(1-x^a)}$

Both $p$ and $a$ are input values (base price and discount aggression respectively).

$b^c$ is a constant derived from two other input values (not listed - maximum discount, and minimum units for maximum discount)

So, we can assume that $p$, $a$, and $b^c$ are all constant values.

Can we rewrite this equation so that it can be generalised to $y=f(x)$ form?

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I solved this to be $y = pe^{(1-x^a)\ln(b^c)}$, but it turns out an earlier equation that fed into this one was wrong. Back to the drawing board for me :)

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    $\begingroup$ Please use the edit link on your question to add additional information. The Post Answer button should be used only for complete answers to the question. - From Review $\endgroup$ – hardmath Mar 16 '17 at 0:47
  • $\begingroup$ This the the answer to the original question I posted, therefore it is the answer. The fact that I got something wrong outside the scope of this question doesn't invalidate this answer $\endgroup$ – e_i_pi Mar 16 '17 at 0:51
  • $\begingroup$ If you feel that rewriting $pb^{c(1-x^a)}$ as $pe^{(1-x^a)\ln(b^c)}$ answers the Question, then perhaps you should edit the Question and Answer to explain to Readers how this amounts to a "generalized... form". Both seem to give expressions $y = f(x)$, and since they are related by equality, the notion of generalizing seems unattained. $\endgroup$ – hardmath Mar 16 '17 at 1:01

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