so simple linear equations such as ohm's law do not apply.
Well it depends on how you look at it.
In the example above I just did the simple calculation of how much energy is needed to be stored in a capacitor. But as I said you can't squeeze it all out. So to get a better idea you have a residual energy at say 7V when it stops working, and the actual energy you get from a fully charged capacitor at 12V. So the available energy is simply the difference between the two. You can use this to see how long you can keep supplying 100mA before the voltage drops to below working. There is no need in this case to evoke exponential decay of the voltage because that is not what you are interested in. The trick is remembering that coulombs are measured in amps per second:-