<pedantic> The year 2100 is still in the 21st century, not the 22nd. </pendantic>
No it IS the 22nd century. Years are measured as floating point values, not integers.
The idea that you can endlessly extrapolate from a short period
of our development is absurd. When we approach the physical limits of the universe with our technologies, the exponential growth will hit a stone wall. Even if that doesn't happen, if aliens came and gave us a technology that's a billion years ahead of us, the exponential curve will commit suicide and eat her own babies.
The whole idea that anything looks exponential, therefore it must be exponential, is flawed. If we applied that to human population, which doubles in 50 years, we'd be 2 trillion by 2400. A curious fact, but a logistic curve
looks exactly like an exponential one, together with an infinite number of other curves. The only thing that makes you favour the exponential is Occam's razor – it's simpler. Well, in this case, it's just too simple to fit even what we know.
There are physical limits both in the direction of miniaturisation, and in the direction of scale. There's a hard limit set by plank distance, plank time and the numbers of particle in the universe. You can never ever go beyond that. Even if those limits can be broken, you will probably just reach another one. Your best option to somehow witness endless exponential advancement is if you got extinct every time you hit the wall, thereby surviving only by the virtue of quantum immortality in a universe where the wall doesn't exist, and this doesn't sound comforting at all regardless of whether MWI makes sense or not.
People get easily dazzled by technology these days, when all they're really looking at is a sudden orgasm of technological progress that occurred really in the last sixty years or so. There's nothing to indicate this is anything more than an industrial growth spurt that won't eventually plateau and remain relatively static with only minor improvements for the next couple of centuries (which is pretty much what happened after the paradigm shifts in the bronze age, the iron age and the opening of the industrial age). IOW, we're at the very beginning of the Silicon Age and we think we've got it all figured out; we're probably another two hundred years short of the Utility Age where all of our technology is converted to programmable swarms of virus-sized robots.
For 2100, I am making three predictions
1) Rich people will get richer
2) Poor people will get poorer
3) The United States of America will collapse into a puff of irony.