What I want to convey is that the growth function will be somewhat similar to y= c + ax^n (ignoring/collapsing into c the linear and higher order terms) rather than just y= ax^n.
The c here is robots produced via humans. I predict c will easily touch a million in 5 years with or without human help.
Even if the later bots can do only 50% the work of humans, we will still exponentially grow the robots until the humans become a bottleneck. And that 50% capability is also expected to grow exponentially.
Gemini 1.5 pro already beats most humans in most benchmarks, combine it with Sora which has a great visual world model, add some logical reasoning(architecture or scale), memory and embodiment(so it can experiment and test) and you pretty much have the seeds for an agi.
My optimistic/most probable prediction about the growth rate say it's
Regarding the last part:
My bad, I speed read your comment and didn't focus on the exponential calculations. An exponential growth is just x^n. Both x(multiplication rate(?)) and n(units of time) can be manipulated.