[msbarnett]

Who said anything about f?

I said "power consumption increases exponentially with clock speed" not "power consumption increases exponentially with f". That any modern processor has to crank up V to crank up its clock speed is a given.

Hence, power consumption is exponential with clock speed (which is achieved by cranking up both V - the polynomial term in P – and f).

(Which, fine, if you want to be pedantic, is polynomial growth, but that changes nothing about the point, which is that you have to burn a shitload more power at 5 GHz than at 3.2 GHz, because your consumption isn't scaling anything close to linear).

[megous]

Clock speed is just f.