I thought that the function will follow the Square-cube Law since we heat water at the surface (which is x^2) while we heat the volume (which is x^3) as it happens in animals according to Bergmann's rule. I did some home experiments and got a linear dependency (the kettle is heated at the bottom by stove):
volume (ml): 150 300 450 600 900 1200 1800
time (s): 90 130 190 260 370 540 675
My explanation: while we heat the surface of the kettle, the water moves inside it – cold water descends while hot water goes up. Therefore we don't heat at the surface, we heat the whole volume of water at every moment of time. If water molecules were not moving up/down, it would've followed the Square-cube Law.
In animals the molecules are not freely moving. Of course there is a blood stream, but when the blood plasma is getting out of the vessel it's still moving by diffusion. And there is also a cell membrane that slows down water flow even more. Also blood has a lot of proteins which are not conducting heat as good as water. So overall animal is very different from the kettle with respect to heat exchange through the surface.
Best Answer
Usually, for a "regular" container such as a pot or kettle, most of the heat transfer occurs through the bottom of the container, and the heat transfer rate is pretty much independent of the amount of water in the kettle. This means that, with constant heat input the time to boil will also be roughly proportional to the volume of the water.