In a general case P = V^2 / R That said, at the manufacturing scales of these parts leakage in the transistor can be as big a power consumer as the switching.

In a general case P = V^2 / R That said, at the manufacturing scales of these parts leakage in the transistor can be as big a power consumer as the switching. Leakage current increasing as voltage increases at a rate that is of the order ~e^Vth I wouldn't really say its strictly either exponential or quadratic, you'd have to know a lot more about the process and the implementation to know how significant leakage current is in the design.