I was doing a textbook question on how the power of a bulb varies with the potential difference across it. I plotted this graph:
(V is on the x axis and P is on the y axis.)
I was then told that this graph obeys the relationship $P=kV^3$ (note that for ohmic conductors the relationship is $P=kV^2$, where $k=\frac1 R$), and I was then told to explain this relationship. I'm not terribly sure where to start; I know that increasing the voltage increases the temperature of the filament and therefore the resistance, but doesn't that mean the current decreases, therefore decreasing the power of the bulb?
For those of you in the British education system, I'm just starting my A level in Physics (which means I'm 17 years old for everyone else), so a decently non-technical answer would be appreciated...