# The tutor begins an exploration of the changing feasibility of solar energy.

There is a graph provided by Scientific American 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.

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

lnw=mt+b

where t=time, while w=Watts.

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

ln4.2=m(0) +b

giving

ln4.2=1.4351=b

m is solved by the slope formula:

m=(ln38-ln4.2)/(28-0)=0.0787

We arrive at

lnw=0.0787t + 1.4351

Taking the exponential of both sides, we get

w=e^(0.0787t + 1.4351)

This can be rewritten, by an exponent law, as

w=e^(1.4351)e^(0.0787t)

which becomes

Watts=4.2e^(0.0787t)

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.

I’ll follow up some implications of this analysis in future posts:)

Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC.