These graphs look linear to you?

https://blog.stuffedcow.net/2012/07/ivy-bridge-power-consump...

https://qph.cf2.quoracdn.net/main-qimg-61820a6b86759c354d41d...

These graphs look like they depict f only scaling?

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).

Clock speed is just f.

P = V^2 * f, yes, but V and f are correlated. You can't increase f without also increasing V, hence: exponential scaling.

That's still a polynomial, not an exponential

That's polynomial scaling, not exponential.