Time vs. Temperature - What changes what?
One fundamental error in this question: 400 degrees is not twice as hot as 200 degrees. Temperature is a measure of the kinetic energy of the particles involved. The only scale on which you can do the kind of ratio you are imagining is Kelvins - you have to measure from absolute zero.

400 F = 477.59 K
200 F = 366.48 K


so the kinetic energy of the air in the oven is only about 477/366 = 1.3 times as high at 400 F as it is at 200. For simple cases, like how long it takes to evaporate a pan of water, 1.3x is probably pretty close to right, but as is pointed out above, there are a whole host of other variables that come into play with real food.



So ...

Bake time variations for a recipe that calls for 400 degrees for 30 minutes converted to a 450 cooking time and a 350 cooking time:

400 Farenheit = 477.594 Kelvin

477.594 x 30 minutes = 14327.82 HeatPoints

450 F = 505.372 K

14327.82 HP / 505.372 K = 28.35 or 28 minutes 21 seconds