What the %&#@?* does exponential mean?

Our visitor from a distant galaxy wonders at the number of things, ideas and events on planet Earth that are reported as growing exponentially. No day goes by without reference to the demand for a product, the incidence of white collar crime, debt growth, or a particularly virulent disease all increasing at an exponential rate.

Exponential is defined as when the growth increases at a fixed rate over time.  For example the number of crows in a murder of crows is doubling every day, or house prices are increasing three fold every five years,  or new cases of Ebola are quadrupling every week.  Our alien friend is further puzzled by an article in a communication’s magazine, stating that the use of cell phones is growing exponentially.

Using her ultra-modern communicator,  she asks home base, many light years away, about this conundrum on planet Earth and how this growth rate of cell phones would manifest itself.

She receives a graphic,  displayed above. The horizontal red line indicates the surface area of the planet, water included; the blue line indicates the area covered by typical cell phones if they double in number every day and are laid down in a single layer side by side. The vertical axis is the surface area of the earth and the horizontal axis is the number of days over which the doubling occurs.

Ms. Alien is very concerned because planet Earth will be completely covered by cell phones in about forty days. Predictably she flees the planet, recommending to her superiors that this is not a place worth colonizing.