Sure, if you model intensity as a variable \(I(t)\) then the most natural fit isn’t a pure \(e^{I}\) but a sigmoidal curve like \(\frac{1}{1+e^{-k(I-\theta)}}\), so you get a plateau at the maximum sustainable load. But you’d still need to calibrate \(k\) and \(\theta\) against heart‑rate data, or you’ll just be chasing your own shadow. And don’t forget the time‑delay factor—your muscles don’t react instantaneously, so an integral term might be required if you want the model to be physically realistic.