I don't believe we will. Exponential growth is going to make it more likely that we will get some sort of strong aware entity before we figure out how to merge. Also it still leaves the problem of transcendence.

Well, Moore's law is ending within 10 years (I'm fairly sure that you can't have a transistor smaller than an atom), so, I'm not sure why I would expect that computational power would continue to grow exponentially.

Moore's law is about a particular way of implementing computation machinery, not computational power. There are many ways of building computing machinery - if one path becomes impassable we can move down another.

Alright, sure, I guess some other sort of technology could be used.

But Koomey's law (amount of computation per amount of energy doubles about once every 1.57 years) has some hard boundaries that aren't all that far off. Landauer's principle / the Landauer bound will stop Koomey's law for irreversible computation by 2048.

And even for reversible computation there is a limit in the Margolus–Levitin theorem , which Wikipedia says (with a [citation needed] ) should run out within about 125 years, which, admittedly, is substantially more than 32 years.

But still,

the earth is finite. Exponential curves about it tend to be more like logistic?

Finitude. Scary stuff.

Sure given the laws of physics there is a finite amount of computation that can be done in a fixed volume. We are still a long way from reaching such limits and the human brain is very far from such limits.

One of the reasons we should fear a super AI is that it will be constrained by the laws of physics and so will want to use all the resources within its light sphere efficiently. Humans are not an efficient structure for computation given the how we evolved so any unconstrained AI would likely not hesitate to reorganise us into a more efficient structure.

I doubt that we know enough to say how exponential growth will go. I do agree that baseline humans will be left in the dust. But that's just how it goes with selection.

Probably in the long-term too.

If you look at the human brain as a computation device and the mind as the software, evolution as the design process, you see that biology has been iterating on the very problem we're trying to solve for hundreds of millions of years, billions if you include abiogenesis.

We don't really understand how the human brain works. We don't know how nature engineered our own initiative. We have a rough idea of the algorithms involved, but understanding those algorithms in detail is not going to be easy.

It's always going to be much much easier to fix the human brain's limitations than it will be to re-engineer a new one. So the economic case for strong AI isn't ever going to really exist, because first we have to build the world where human-level AI is a thing.

I think "rough" is understating it. Galileo finding different sized objects fall at the same rate, knew more about gravity than we know about intelligence. By analogy, in terms of gravity, our understanding is at the "Things fall downwards" stage. The Newton's Laws of Motion for intelligence are a long ways off yet.