Electricity is a renewable resource. Mankind has increased electricity exponentially.
Most electricity is created using coal. Coal is not renewable on non-geologic timeframes. It is expected to last only another few hundred years.
Or another example, Dubai is a city that grew out of the sand within 15 years. Population exploded and with it the demand for clean water exploded. Your theory would state that it'd be impossible for Dubai to grow exponentially, because it would run out of water - water being produced only in a "linear" fashion.
But of course, Dubai doesn't care about your theory. The solution was simply to build more desalination plants, thus increasing clean water exponentially along with population.
Dubai went bankrupt in the housing crash, and had to be bailed out by it's neighbor Abu Dhabi, which owns the energy resources necessary to run desalination plants.
LOL so we only have another few hundred years to find alternatives to coal? Yikes we're doomed!
The fact that Dubai's government needed a huge loan from Abu Dhabi doesn't invalidate my point. Abu Dhabi experienced similar growth and the clean water/desalination issue is the same there. The point is that resources can be and are produced to meet the needs of humanity.