Solving for exponents in proportionality

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Discussion Overview

The discussion revolves around determining the exponents in a proportionality relationship involving two variables, A and B, in an experimental context. Participants explore the formulation of the relationship and methods for solving for the constants involved.

Discussion Character

  • Exploratory, Technical explanation, Homework-related

Main Points Raised

  • One participant proposes a model where the result is expressed as Result = (A^alpha)/(B^beta) and seeks validation of this approach.
  • Another participant suggests that an additional constant is necessary, leading to the formulation Result = k * (A^alpha) * (B^beta).
  • A participant inquires about methods for solving the equation, expressing a preference for experimental determination of the constants alpha, beta, and k.
  • Another participant recommends taking logarithms of the equation to simplify the process and suggests using a least-squares fit if more data is available.

Areas of Agreement / Disagreement

Participants generally agree on the need for an additional constant in the formulation, but there is no consensus on the best method for determining the values of alpha, beta, and k.

Contextual Notes

The discussion does not resolve the specific methods for solving the equation or the implications of using trial and error versus statistical fitting techniques.

Who May Find This Useful

Researchers or students involved in experimental design and analysis, particularly those interested in proportional relationships and regression techniques.

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In an experiment I am performing, I observed the following:

Result is directly proportional to A
Result is inversely proportional to B

So, I assume two constants, alpha and beta such that:

Result = (A^alpha)/(B^beta)

Now, if I know I want to solve for alpha and beta but is this the right approach to take to get the value of Result for any given A and B?

(Actually, I could have assumed Result = k. (A/B) but I am not sure that my result follows such a simple proportionality which is why I assumed alpha and beta). Any input on this is appreciated. Thanks
 
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You also need a constant out front, for a total of 3 constants to be determined.
 
So that means, I should in fact be looking at Result = k. (A^alpha) * (B^beta)? Could you provide me some insight on how to go about solving this equation? I am new to these things so even a direction would be helpful...

I was actually thinking of determining alpha, beta and k on a trial and error basis experimentally but that would take me ages with the experiment I am running...
 
Take logarithms, then it's just a high school algebra exercise to regress three points to it. If you have more data you can do a standard least-squares fit.
 
Understood... Thanks so much for the help :)
 

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