even more pedantically: sub-quadratically since it's being built on a positively curved manifold. As the Pentagon approaches the size of a hemisphere, growth will stop and then reverse.

That's also assuming that the thickness of each ring is constant. If they increased the thickness by a certain percentage relative to the previous band, then you'd have exponential growth.

But the existing rings are equal-width, and wider rings do not make sense (the buildings would get less and less daylight)

Fair point. I guess there's another assumption, that the rings are built at a constant rate. In fact, if we make the typical assumption that the economy grows exponentially (which might hold for all but the longest term models), it could be possible to build newer rings at an exponentially faster speed by constructing more and more of them simultaneously.