>>13825475Yeah, these types of equations are fairly intuitive. The only thing that is non-intuitive is the presence of the e, but that's because the e does not have a direct relevance to the physical interpretation or the particular application you're working with.
It's just a useful quantity for taking exponents because of the properties of e under differentiation. The expression involving e could actually be replaced with a numerically "simpler" value that more closely resembles the actual physical quantities that you're working with, but that would make it a little more convoluted to take derivatives or integrals of the function. This is all very abstract, but if you study the properties of e under differentiation and integration, you'll get what I mean. It just take a little experience with differential equations and basic complex analysis. Logically speaking, it is analogous to working in a different base. E.g. in most contexts we use base-10. Sometimes base-2, sometimes base-16, etc. Sometimes we even use scientific notation, as I'm sure you're familiar, i.e. expressions like k*10^n, where n is an integer. The use of scientific notation doesn't necessarily have any direct empirical significance. It's used because it provides a mathematically more convenient notation, not because it represents some important property of the system we're trying to model. The same thing goes for the number e.
