I'd say that a growth of total computing power to between 10,000x and 10,000,000x of the current one in 20-30 years, followed by stagnation or perhaps a slow growth, seems reasonable
From Wikipedia:
Although this trend has continued for more than half a century, Moore's law should be considered an observation or conjecture and not a physical or natural law. Sources in 2005 expected it to continue until at least 2015 or 2020.[note 1][11] However, the 2010 update to the International Technology Roadmap for Semiconductors predicts that growth will slow at the end of 2013,[12] when transistor counts and densities are to double only every three years.
It's already happening.
Current process size is ~22nm, silicon lattice size is ~0.5nm . Something around 5..10 nm is the limit for photolithography, and we don't have any other methods of bulk manufacturing in sight. The problem with individual atoms is that you can't place them in bulk because of the stochastic nature of the interactions.
Background:
On the most recent LessWrong readership survey, I assigned a probability of 0.30 on the cryonics question. I had previously been persuaded to sign up for cryonics by reading the sequences, but this thread and particularly this comment lowered my estimate of the chances of cryonics working considerably. Also relevant from the same thread was ciphergoth's comment:
Based on this, I think there's a substantial chance that there's information out there that would convince me that the folks who dismiss cryonics as pseudoscience are essentially correct, that the right answer to the survey question was epsilon. I've seen what seem like convincing objections to cryonics, and it seems possible that an expanded version of those arguments, with full references and replies to pro-cryonics arguments, would convince me. Or someone could just go to the trouble of showing that a large majority of cryobiologists really do think cryopreserved people are information-theoretically dead.
However, it's not clear to me how well worth my time it is to seek out such information. It seems coming up with decisive information would be hard, especially since e.g. ciphergoth has put a lot of energy into trying to figure out what the experts think about cryonics and come away without a clear answer. And part of the reason I signed up for cryonics in the first place is because it doesn't cost me much: the largest component is the life insurance for funding, only $50 / month.
So I've decided to put a bounty on being persuaded to cancel my cryonics subscription. If no one succeeds in convincing me, it costs me nothing, and if someone does succeed in convincing me the cost is less than the cost of being signed up for cryonics for a year. And yes, I'm aware that providing one-sided financial incentives like this requires me to take the fact that I've done this into account when evaluating anti-cryonics arguments, and apply extra scrutiny to them.
Note that there are several issues that ultimately go in to whether you should sign up for cryonics (the neuroscience / evaluation of current technology, estimate of the probability of a "good" future, various philosophical issues), I anticipate the greatest chance of being persuaded from scientific arguments. In particular, I find questions about personal identity and consciousness of uploads made from preserved brains confusing, but think there are very few people in the world, if any, who are likely to have much chance of getting me un-confused about those issues. The offer is blind to the exact nature of the arguments given, but I mostly foresee being persuaded by the neuroscience arguments.
And of course, I'm happy to listen to people tell me why the anti-cryonics arguments are wrong and I should stay signed up for cryonics. There's just no prize for doing so.