To give a particular example, the exponential growth of computing power has been a close-enough match to exponential since Kurzweil became famous: It was about 20 years ago that Apple was boasting that their latest PowerMac was banned from export to Cuba because a 1 gigaflops computer counted as a weapon, now they boast their phones do 11 teraflops — compatible with 1.5 year doubling time.
(That said: while I have met someone who expected the exponential to continue past single atom transistors, I do expect it to stop soon-ish; superconducting/3D/quantum computing may replace classical transistors, but I never expect to see multiple transistors on a single atom).
It works until it doesn't.
Extrapolation outside your dataset is only a problem if you take it too far, and how far is “too far” depends on how well you modelled reality with your dataset in the first place.
But this energy is not infinite. Despite all innovations in solar/wind, and assuming efficient storage that does not exist yet, EU won't be able to absorb a 3% decrease in oil+gas importations by 2030. Rystad (https://www.rystadenergy.com/), pre-covid, was forecasting a 2 to 8% decrease in oil and gas import from the EU according to the think tank "the shift project" [0][1].
I won't talk about manpower much because there is still a chance that nothing more heavy than Covid will hit us in the near future, but meals will be hard to get this year in eastern Africa and while this year India did not suffer as much as in 2019, another drought like 2019 next year would be even more disastrous. For information, this winter could have been worse for Africa than 2011, luckily the wildfires and drought in russia were localized further north than a decade ago.
But well, we still have two silver bullets: fusion and renewable hydrolyse.
[0] https://theshiftproject.org/wp-content/uploads/2020/06/Study... complete data analysis
[1] https://theshiftproject.org/wp-content/uploads/2020/06/fig40... short graph.