Huh?
The world's economy has grown by over 50% since 2000.[1]
Be creative: unbounded exponential growth would mean, for instance, that at some point in the future the global yearly energy consumption would be higher than what E=mc^2 suggests for m=mass of the earth.
Other than that, I think it's hard to think of economic growth for periods longer than a few generations.
When economists say that a dollar in 2015 is worth $X in 1066 and we are Y% richer, that's a very leaky metaphor. It's basically saying that a sheep or a loaf of bread cost x in 1066 and people made z every day and if we take our daily salary and divide it by loaves of bread and sheep then we don't really have to consider that we buy ipods and toothpaste and they bought slaves and mutton. It's just nonsensical to try and represent it quantitatively.
So economic growth in the long term is hard to think about in numbers. Say a vaccine for cancer, alzheimer's & diabetes was invented tomorrow. You would be willing to pay money for that and glad of the opportunity. That's economic growth. The researchers uses lithium in their laptops and fossil fuel to keep the lights on, but still I don't think natural resources will bound this kind of thing.
Also, the primary problem is not really the growth itself, but the need for it that is built into the basic assumptions of economy - because if and when we'll eventually hit a speedbump, everything will collapse.
Economic growth is a very theoretical concept. Something doubles our economic growth if we make it and people value it as much as the stuff we are already making. If we invented new Japanese cartoon cat pens so cute and desirable that every person on the planet pays $1000 for it, bam! 7.1 trillion dollar growth. Just remove 7 billion regular pens to make room in the universe, and we're at 7.0999. (assuming no resources were diverted from other things)
Economic growth is kind of meaningless to think about at this scale. But at any two points on a more human scale, it means something.
That said, an exponentially growing (shoe) economy that eats the universe sounds like a Douglas Adams story so maybe you're right.
In the case of 1% growth the second interval is larger than the first, but the third is not larger than the first and second combined (it's still roughly 1/2 that).
It's certainly true that it won't be true for all interval lengths - that is obviously mathematically nonsensical.
In a finite universe, yes, it is clearly nonsense. Exponential growth cannot continue forever in a finite universe, no matter how small the growth constant.
I was saying you can't have growth for which f(n + k) = 2 f(n) for all k > 0 (I believe the only solution to that is f(n) = 0, which isn't what anyone is talking about when they talk about "exponential growth"...). This point was intended, in contrast with what I'd just said about there existing some k - to stress the notion of when the interval is picked.
Apparently, I wasn't doing it well, but that's what I was trying to do.
Whether unbounded exponential "economic growth" is possible in a finite universe is actually a significantly more involved question. It's obviously not possible if "economic value" is bounded, but in principle could be "possible" with finite stuff in continuous space (obviously, economic value depends significantly on configurations of stuff and not just amounts).
All of this is interesting, but I honestly don't expect any reasoning involving hard theoretic bounds to be of any use in determining what's likely over my lifetime, or those of my children.