All lifeforms on Earth, whether it be bacteria or human beings, will reproduce exponentially if given unlimited resources.
This means that the population will continuously double in consistent time periods.
This time period can be just a few minutes in the case of bacteria, or it can be decades in the case of human beings.
However, no matter how long the time period is for a population to double, if exponential growth were to continue indefinitely,
then the population will eventually expand faster than the speed of light, in direct violation of the known laws of physics.
If the number of red balls inside this green sphere continues to grow exponentially, then the volume of the green sphere will also increase exponentially.
Since the volume of a sphere is proportional to the radius raised to the power of three, it takes three times as long for the radius of the green sphere to double as it does for the volume to double.
Nevertheless, since the radius doubles in regular time intervals, the radius is also growing exponentially.
Let’s watch what happens as the radius continues to grow exponentially.
Economists like to use exponential functions to model our economic growth.
However, in a very short amount of time, exponential economic growth becomes impossible on a finite Earth,
and it would not be possible even if humans were to expand far beyond the Earth.
Neglecting the expansion of the Universe…
If we emit light in all directions, the radius of our sphere of light will grow linearly.
The radius of our sphere of light will grow linearly.
All linear functions are eventually exceeded by exponential functions.
No matter how long the time period is for a population to double, if exponential growth were to continue indefinitely,
then the population will eventually expand faster than the speed of light, in direct violation of the known laws of physics.
All linear functions are eventually exceeded by exponential functions.
This also remains true regardless of how small the initial value of the exponential function, so long as the initial value is not zero.
If you start with only one penny, and double it every day, then in one month you will be a multi-millionaire.
One additional month after that, you will have more money than presently exists on the planet.
Similarly, any continuous exponential growth would cause us to run out of resources, long before we have to worry about exceeding the speed of light.
But the most intriguing and the most dangerous thing about continuous exponential growth is the following.
Hypothetically suppose it takes 20 time periods to run out of resources.
(Assuming exponential growth, with consumption of resources doubling each time period.)
If we are living in time period number 15, when approximately 97% of our original resources are still remaining, would we realize that we are about to run out of resources?
Perhaps we have underestimated our resources by 100%, and our total resources are actually twice as large as we previously thought.
But, this would only mean that it will take 21 time periods to run out of resources, instead of 20.
The numbers shown here assume continuous exponential growth right up until the very end,
whereas in reality the rate of growth will decrease as the limitation of resources becomes an issue.
Exponential growth only occurs when the resources are still plentiful.
But with exponential growth, 50% of the original resources are still remaining just one time period before the end,
and this can cause us not to realize that we are about to have a problem until the very last time period.
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