Exponential growth is the growth of a system in which the amount added to the system is proportional to the amount already present. The bigger the system, the greater the increase will be.

Compound interest is a good example of exponential growth. Technology grows exponentially and therefore the rate that our technological advances are achieved is increasing. As the rate of our advances continues to accelerate, the future continues to come faster than we traditionally expect with our linear thinking patterns. It’s also why such growth can be hard to grasp. Once we grasp it, it becomes clear that the possibilities are unfathomable and holds promise to an abundant future.

Exponential curves start slowly and then skyrocket toward infinity. Exponential growth is simple doubling. 1 becomes 2, 2 becomes 4, 4 becomes 8, but, because most exponential curves start out well below 1, early growth is almost always imperceptible. When you double .0001 to .0002 to .0004 and .0008, all of these plot points look like zero on a graph. At this rate, the curve stays below 1 for a total of 13 doublings. Only seven doublings later, that same line is above 100. And it’s this kind of explosion, from meagre to massive and seemingly so quickly, that makes exponential growth so powerful.

According to Ray Kurzweil, we are not evolved to think in terms of exponential growth. Exponential growth is not intuitive and linear thinking is hardwired in our brains. Exponential growth of information technologies is even greater and we are doubling the power measured by price-performance, bandwidth and capacity about every year:

An analysis of the history of technology shows that technological change is exponential, contrary to the common-sense “intuitive linear” view. So we won’t experience 100 years of progress in the 21st century — it will be more like 20,000 years of progress (at today’s rate). The “returns”, such as chip speed and cost-effectiveness, also increase exponentially. There’s even exponential growth in the rate of exponential growth. Within a few decades, machine intelligence will surpass human intelligence, leading to the Singularity — technological change so rapid and profound that it represents a rupture in the fabric of human history. The implications include the merger of biological and non-biological intelligence, immortal software-based humans, and ultra-high levels of intelligence that expand outward in the universe at the speed of light.

Albert Bartlett, who was an emeritus professor of physics at the University of Colorado at Boulder, USA, put together a now famous lecture titled "Arithmetic, Population and Energy" in 1969. The lecture, available broadly on the internet, begins with the line:

"The greatest shortcoming of the human race is our inability to understand the exponential function."