Nothing conclusive, but:

1. If we look at rate of change over the last few thousand years, it doesn't seem completely unreasonable to extrapolate that forward.

2. It's hard to argue that no more breakthroughs can possibly be made in physical computing architecture or computer science, though admittedly it's equally hard to argue breakthroughs definitely will be made. However...

3. Modern industry is heavily incentivized toward AI advancement, because of the optimization capabilities it provides. Where such incentives exist, barriers tend to dissolve.

It doesn't really matter whether it continues exponentially, even if the singularity is hundreds of years away the dangers are mostly the same.

The exponential hype?

Pure hype.