I point this out not because I think this history must be our destiny, but instead to raise awareness that much more must be done to avoid that destiny.
I don't know much about the field, but given the vast investments and land needed for country level solar projects I would argue the growth rate is much more likely to be linear, in which case it looks like it won't be overtaking oil this century.
It's relatively easy to make large percentage gains when the current amount is so small.
Looking longer-term there will be growth slow-down when wind/solar reaches a larger scale due to the intermittent nature of the energy unless we can figure out how to deal with this. Currently dealing with it requires lots of gas peaker plants, hydro (which has its own environmental damages) or batteries (the resources required to produce and continually replace these are not sustainable but hopefully the net carbon emission can stay low). Malaysia recently had to stop incentivizing solar because their grid couldn't handle it.
Considering we're going to see mass adoption of electric vehicles in the next 5-20 years I think that will happen even more quickly.