I don't understand what you're saying. Logarithmic, exponential, it doesn't matter what shape the curve is or how fast you get there - all "growth" we care about is ultimately backed by expenditure of physical resources, which are clearly limited. If you redefine "the economy" in such a way that it's not limited, you also break its connection to the real world.
Honestly, all this talk about money is distracting from the core issue, which is that we are unsustainably increasing our consumption of limited resources.
Honestly, all this talk about money is distracting from the core issue, which is that we are unsustainably increasing our consumption of limited resources.