There is a graph provided by Scientific American<\/a> that shows the Watts one might get for $100 from solar cells by year. As they point out, it’s a logarithmic graph; here I’ll show some analysis.<\/p>\n The two points I’ve fetched from the graph, in the format (year, watts) are (1980, 4.2) and (2008,38). The linear shape is accomplished by the relationship<\/p>\n lnw=mt+b<\/p>\n where t=time, while w=Watts.<\/p>\n I’m imagining 1980 as year 0; the two points mentioned earlier become (0,4.2) and (28,38). Then b, the lnw intercept, is given by<\/p>\n ln4.2=m(0) +b<\/p>\n giving<\/p>\n ln4.2=1.4351=b<\/p>\n m is solved by the slope formula:<\/p>\n m=(ln38-ln4.2)\/(28-0)=0.0787<\/p>\n We arrive at<\/p>\n lnw=0.0787t + 1.4351<\/p>\n Taking the exponential of both sides, we get<\/p>\n w=e^(0.0787t + 1.4351)<\/p>\n This can be rewritten, by an exponent law, as<\/p>\n w=e^(1.4351)e^(0.0787t)<\/p>\n which becomes<\/p>\n Watts=4.2e^(0.0787t)<\/p>\n The exponential argument 0.0787t suggests growth of 7.87%. Rounding it to 8%, and applying the rule of 72, the Wattage per $100 should double about every 9 years.<\/p>\n I’ll follow up some implications of this analysis in future posts:)<\/p>\n