Exponential growth of recursively self-improving AI happens simultaneously in several dimensions.
1. Better algorithms, more efficient, faster, more capable.
2. Better hardware, for example bespoke chips for each particular common computation. Could figure out molecular computing as Drexler predicted.
3. Recruit more computer capacity. Every networked computer could be used by a well-funded AI willing to pay enough.
4. Applying AI to exponentially increasing quantity of tasks by progressive decomposition of tasks into subtasks. Each worked in parallel as needed.
5. AGI would interact with the physical world with robotics that it designs, manufactures and operates.
If this is correct, then we could expect what AI-safety folks name "FOOM". Link: https://www.lesswrong.com/posts/t8dtuYXPhwt93PstB/requiremen...
If encouraged, as opposed to restrained, FOOM could happen days after AGI has the means to improve in the above dimensions. The hardware dimension would be limited at first by the human supply chain, and those limits would be gone when AGI runs its own supply chain - perhaps within a year after AGI.