Assuming that humans somehow would work like that, this is physically impossible. For example, the United States has had a remarkably steady growth of about 3% increase in total energy since 1650. Let's say that the world grows at this pace. If the massive hurdle of resource shortages are somehow overcome, there's still the second law of thermodynamics to deal with. Quite simply, no matter what energy source is used, there's going to be waste heat. Earth will be as hot as the surface of the Sun in only a couple of centuries. The amount of energy used will exceed that of the entire Universe in only a couple of millennia. Such is the power of the exponential function.
Oh god, that article again, I'm just going to copy paste the exact response to this I just made somewhere else.
Meanwhile, back in the real world, a physics professor has
pretty conclusively proved that economic contraction due to energy constraints is literally inevitable over even a relatively short-term timescale (ie this century).
This article gets posted over and over again despite being incredibly flawed on a fundamental level since it basically assumes a constant exponential increase in energy usage forever and ever (2.5%), as indicated by the first graph posted in the article:
This basically the classic, take the average past trends (over 400 years), assume it will remain constant, and then project X years into the future which is hilariously inaccurate because things like energy usage or size of the economy do not grow at constant rates. The US and much of the first world, for instance, have seen energy usage/per capita -drop- since the high point of the 70s. -Despite- no permanent rise in unemployment and constant, exponential growth in per capita income. It seems once industrialization have completed and everyone has cars there isn't much demand for energy intensive goods any more and people instead prefer energy inexpensive services.
At the same time, the birth rate in the US have fallen to be around replacement, which means that, discounting immigrants (which is really just shuffling people around and you can restrict the number of them coming into the country if you really want to), net energy usage have -fallen- in the US because natural population growth is 0 and energy usage per capita have fallen. Energy usage tend to level off after a while.
Energy usage have greatly increased in the developing world, but that is because they are undergoing periods of industrialization and extensive growth which requires a lot of energy. Even given the best cause scenario for China and India similarly growth in energy usage is not going to last once their economy transitions from middle to high income status. And if they don't, that means their economic growth have stagnated which means their energy usage is not growing by 2.5% per year either.
Ultimately, energy usage have increased rapidly in the last few centuries because of the industrial revolution, so really, for the projection to make sense you essentially have to assume humankind undergoes new equivalents of industrial revolutions: 1790-1970 for as long as the projection last.
tl;dr: increase in consumption does not nessessarily lead to increase in energy usage, services, for instance, takes next to no energy but represents additional employment.