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I am reading an analysis on circuit board trace heating, and have found a source for a general temp rise vs current equation that matches measured IPC 2152 closely. However, I am having trouble following the steps from Eq. 2-3 to Eq. 3-1. I understand that the trace resistance is inversely proportional to the area, but don't know how the model picks up the a1, a2 exponents. Is this just a curve fitting thing or is it some algebraic trickery?

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Source: https://www.ultracad.com/articles/pcbtempr.pdf

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It's just empirical curve fitting.

a1 and a2 are undetermined constants that are approximately 1.0 to 1.5

and

After a little work it was determined that the best fit for these curves was an equation of the form: ...

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