As explained before, most growth of innovation can be mathematically captured by a relative straight forward growth curve. Mostly this growth curve can be properly modelled with an S-curve . Let us now for the sake of fun have a look at the global development of the number of motor vehicles. The numbers originate from a series of sources [4-12] and the fitted curve is a three parameter S-curve .
With fitting the S-curve, two quite bold assumptions were made:
The first assumption is that the final global car-saturation level is assumed to be equal to the 2010 car-penetration level of the USA. This level is about 808 cars per 1000 inhabitants .
The second assumptions is that in 2050, the global population is assumed to reach and stabilize at 10 bilion [10 x 10^9] inhabitants.
These assumptions are leading to a global saturation level of about 8.08 billion motor vehicles.
That the world is striving for a wealth comparable with that of the USA is astonishingly showed in the numerous presentations of Hans Rosling . The assumption that in that line of wealth development, the world is striving to a similar penetration level of cars appears not to be too far fetched. Following these assumptions, the global number of motor vehicles will resemble the S-curve presented in the following figure:
In this figure, besides the statistical data available from numerous sources [4-12], two forecasts are given as well. The 2030 forecast in this figure originates from Dargay e.a.  and corresponds pretty well with the fitted S-curve. The 2050 forecast in this figure originates from the 2011 OECD international transport forum  and appears to be on the conservative side, when compared to the S-curve forecast.
From the assumptions made, we are going to have about eight times as much motor vehicles on the planet as we have now.
Further the number of vehicles on the planet is still growing ever faster, until about 2050, where the fitted curve changes from concave to convex.
Interestingly, these cars are in the future likely not to be all fossil fuel powered, because in fossil fuel production we are about to reach peak production. In the following figure is the yearly produced mineral oil is presented. It can be seen that the production is, though still increasing, is in its convex phase, past its inflexion point . The data from 2012 and 2013 are the forecasts given by the IAE . With a slowing growth of mineral oil production and an increasing growth of the number of vehicles, soon there is simply not enough mineral oil to feed all these vehicles.
So here there is ample space for innovation! More efficient vehicles and alternative energy sources, I cant wait to see them coming!
 The Rise and Fall of Infrastructures, A. Grübler (1990) http://www.iiasa.ac.at/Admin/PUB/Documents/XB-90-704.pdf
 Analysis of Logistic Growth Models, A.Tsoularis, Res. Lett. Inf. Math. Sci, (2001) 2, 23-46