Earlier quoted context omitted.
The sun will burn out at a fixed time regardless of how much or little energy we harvest from it. Assuming energy demand growth of 5% per year, we have enough land-based actinates for less than a century of energy usage in fast breeder reactors (if you prefer 2% annual demand growth, it's enough for about 2 centuries). Seawater uranium buys you more time, depending on how you extract it, but hundreds of years and the…
A hundred years would give us plenty of time to develop alternative energy sources (fusion?). The fossil fuel age also last(s/ed) for about that long.
How has energy consumption behaved before around the time of paradigm shifts and plentiful "free" energy?