Kleiber's Law states that metabolism scales to mass to the negative quarter-power. From this it follows that an elephant which is about 1000 times heavier than a chipmunk would, on an average, have metabolic rate 1000 ^ (1/4) i.e. ~5.5 times that of the chipmunk.
Geoffrey West applied Kleiber's Law to Cities and observe similar scaling of a city's size to it's energy utilization. So a city A 50 times larger than city B would utilize 50 ^ (1/4) i.e., ~2.6 times as much energy.
Steven Johnson's book Where Good Ideas Come From mentions that the only aspect of a city that didn't follow the same pattern, but a positive instead of negative quarter-power scaling, was innovativeness of a city w.r.t. it's size. He then goes on to say a city 10 times larger than another would be 17 times as innovative. Also, a metropolis 50 times larger than a town would be 130 times as innovative... Having difficulty following how the math works out in these cases.
