An exponent models things locally, at an appropriate level of detail for modeling them locally. An S-curve won’t actually be an S-curve, there will be a lot more data than that in the real thing, omitting the data specifying when the exponent slows down is no different. Simpler models are often more useful, even when you do realize they have a limited scope of applicability.
Your argument doesn’t make sense to me. You’re saying the exponential models things “locally”, but then so can a sigmoid. You say an S-curve won’t actually be an S-curve, but neither will an exponential. An exponential function that fits data is not that much simpler than a sigmoid function, and importantly the exponential will be wrong in a non-specific way (we just know that after some unspecified point exponential growth will break down). The sigmoid is at least wrong in a specific way that allows us to say something about where we made a mistake in modeling how growth will end (and because growth always eventually ends, failing to model it is making an incomplete model that clearly confuses a lot of people, because there’s no end to people who act as if the growth of something will never end).
An exponent models things locally, at an appropriate level of detail for modeling them locally. An S-curve won’t actually be an S-curve, there will be a lot more data than that in the real thing, omitting the data specifying when the exponent slows down is no different. Simpler models are often more useful, even when you do realize they have a limited scope of applicability.
Your argument doesn’t make sense to me. You’re saying the exponential models things “locally”, but then so can a sigmoid. You say an S-curve won’t actually be an S-curve, but neither will an exponential. An exponential function that fits data is not that much simpler than a sigmoid function, and importantly the exponential will be wrong in a non-specific way (we just know that after some unspecified point exponential growth will break down). The sigmoid is at least wrong in a specific way that allows us to say something about where we made a mistake in modeling how growth will end (and because growth always eventually ends, failing to model it is making an incomplete model that clearly confuses a lot of people, because there’s no end to people who act as if the growth of something will never end).