Explaining the exponential growth in Technological change

In the 1950'sThe Nobel prize winning economist Solow discovered that about 90% of all economic growth in the USA between 1909 and 1949 was directly attributable to technological invention and innovation. http://nobelprize.org/nobel_prizes/economics/laureates/1987/press.html

There is a huge area of economic study related to this discovery and how best to finance R&D- For example, should it all be government funded or privately funded ?

Anyway, my own view is that the exponential growth of knowledge, technology and innovation is directly related to the number of human brains on the planet. As population increases, less communal brain power is dedicated to getting food, and more thinking time is dedicated to things such as how to improve a jet engine's fuel efficiency, or how to make a microprocessor smaller for example. So as population increases, the rate of change in technological innovation also increases. For this reason I am optimistic for the human race. The computing power of 9 billion brains by 2050 are sure to solve most of our pressing problems about environment, sustainable development and the improvement of the human condition.