You cannot add/subtract things which don’t have the same dimensions. Further, such formulae cannot forbid negative answers even though you’re trying to model st

You cannot add/subtract things which don’t have the same dimensions. Further, such formulae cannot forbid negative answers even though you’re trying to model strictly positive quantities. That naturally lends to multiplication. If you want to exponentiate, you can only use dimensionless quantities in the exponent (and that kind of dependence does pop up sometimes, in interesting places). But the exponential dependence means very low sensitivity for small values for the exponent, so (by Taylor approximation) you might get away with using a constant, or redefining variables (by subtraction/rescaling) to come back to the multiplicative format. In other words, you’re taking the log on both sides and doing dimensional analysis with the new variables.