Energy usage per point of GDP = f(t)
Then we can obviously construct a hypothetical scenario:
lim t->inf g(t) * f(t) = C
This is obviously possible if one flips it over, making economic growth depend on the rate of which we reduce the energy cost for producing a dollar of GDP.
This obviously means that production must be decoupled from the sheer AMOUNT of physical goods, as those are necessarily limited.
To increase GDP, we do not need to increase the amount we produce but the value of what we produce.
Sure, one way to increase GDP would be to produce two cars for the same resource use as one car would need. And that has limits.
But if I can produce a rocket that can propel something to orbit with the resource use of a car, I’m am not only enabling more rockets being built, but also actively reduce the energy cost of one.