Of course, but in cases where there's a defined endpoint we also know that the decay from the exponential looking phase is going to happen well before we get there.
i.e. the solar industry won't start installing solar panels at an ever higher rate if the amount of solar penetration is almost 100%. In fact the relative value of installing panels will decline as we get nearer to it. Arguably that's already happened - i.e. power prices going negative scrapes a lot of the shine off private industry funding them.
Versus say, a natural process where while this might happen, the bounds aren't limited by humans making economic decisions for themselves (which of course, when you think about it also implies dangers in extrapolating effects of natural processes like climate change - the rate of some downstream parameter going up and looking linear and shallow could just be a very large system in the middle of moving into an exponential phase which extends well beyond our ability to manage it).
to look at it another way, when will we have so much solar energy production that it's hard to find a market for more solar energy at costs similar to present plant costs? right now a megawatt-hour of solar power costs usually about 25 dollars, half to a third of the cost of a megawatt-hour of power from coal or oil. the energy transition has, roughly speaking, cut the cost of energy in half. in sunny places, it's even cheaper. that means many energy-intensive industrial processes that were previously unprofitable have just become very profitable. how will that reshape the economy?
it's hard to say in detail, but clearly, as those ramp up, energy demand will increase
if you think the answer is '100% of current world electrical generation' or even '100% of current world marketed energy consumption' you've imported the implicit assumption that this seismic change in the energy market, unprecedented since the early days of the steam engine, won't reshape the economy at all and won't increase energy demand at all. this seems like a very implausible assumption
a more plausible endpoint is '100% of the sunlight that hits the earth'—once we start approaching that endpoint, we'll have problems like oxygen-producing algae dying off in the ocean because it's not getting any sun. that starts to become a problem at roughly 1000× current world marketed energy production, 10 doublings, so, around 02050
The shape of the curve is a bit of a red herring, unless additional context is considered. Decay could mean we have succeeded in decarbonizing the entire power sector, which is a signal of success. Or decay could mean California has finally built all the solar it needs but no other states are following in California's footsteps, which is a signal of failure. Both are instances of decay that signify very different situations.
You are correct though that a naive prediction of constant doublings is definitely wrong. China is showing signs of slowing over the last month due to transmission and storage bottlenecks in a few locations. BNEF has an article about this.
i.e. the solar industry won't start installing solar panels at an ever higher rate if the amount of solar penetration is almost 100%. In fact the relative value of installing panels will decline as we get nearer to it. Arguably that's already happened - i.e. power prices going negative scrapes a lot of the shine off private industry funding them.
Versus say, a natural process where while this might happen, the bounds aren't limited by humans making economic decisions for themselves (which of course, when you think about it also implies dangers in extrapolating effects of natural processes like climate change - the rate of some downstream parameter going up and looking linear and shallow could just be a very large system in the middle of moving into an exponential phase which extends well beyond our ability to manage it).