Linear growth is a linear correlation between a parameter and its growth rate. In these systems, the rate of change is constant. On the contrary, exponential growth is an exponential correlation between a parameter and its growth rate. Exponential growth is much faster and is observed in systems with unlimited upside potential. For example, the rate of science growth has been exponential over the past few decades with an exponentially upward curve. This progress is sustainable as long as humans are constantly innovating and generating new science.
Ray Kurzweil, a famous scientist, and inventor argues that the rate at which computing power grows is exponential. There is historical data to support this notion. Kurzweil believes that the exponential growth of computing systems continues to the point that computers start improving their own system without human intervention. In other words, the computing power of a robot exceeds human potential. This is usually referred to as Artificial General Intelligence (AGI) or Singularity. AGI is a case where a robot is capable of interacting with the world as well as any human. Ray Kurzweil scrutinizes this phenomenon in his book called "The Singularity Is Near". However, AGI is still controversial and speculative in nature.
Kurzweil's prediction of the exponential growth of computing systems is an example of Moore's Law. Gordon Moore, the co-founder of Intel Corporation, first demonstrated that the number of transistors on integrated circuits doubled every year since the adoption of computer chips. "The Beginning of Infinity", authored by David Deutsch is another book that argues the exponential growth of computing power and supports Moore's Law.