Please. Amazingly, new landfills become economical to open as Y approaches zero, and we always seem to find a place to put our garbage. We really aren't in danger of running out of land for that.
For oil, I figure much the same takes place. Once an energy company has a certain number of decades of proven reserves under its control, why waste money on intensive new exploration to confirm even more? At some point, the company will decide it is running too close to exploiting their own proven recoverable reserves, and will search for more. So in any given year you could write a story that we will run out of oil at anticipated rates of consumption in X number of years. X seems remarkably stable over the decades.
And our ingenuity finds ways to exploit resources that we can't imagine. Who would have guessed this 10 or 20 years ago?
The [Canadian province of Alberta] is on track to become the world’s second-largest oil producer, after Saudi Arabia, within 10 years.
Or fracking, which is opening up American natural gas and oil fields to exploitation we didn't dream was possible? And which will spread to the rest of the world to exploit their "exhausted" energy resources.
Who knows what we will do in the future? I sure don't know. And nobody has known. Heck, maybe we'll burn our garbage in facilities that turn out cheap fuel cells with the energy produced?
We will find ways to produce energy. We always have.