. There used to be things called tri-lights with 3 settings (low, medium, high); they had 2 filaments which would give off light and you would turn a knob to turn on 1 or the other or both. Let's imagine that you always use the lamp on high till one of the two filaments burns out and then you use the filament which has not burned out. Imagine that each filament lasts an exponentially distributed time with rates l (this is for the filament producing the low amount of light) and m(for the medium amount of light - high results from both being on and working). When the second filament burns out you buy a new light bulb and once again use the light on high. I want you to tell me the proportion of time, in the long run, that you have the light bulb giving off each of low, medium, and high, amounts of light. In doing this problem half the marks are for the algebra, calculus and arithmetic that get you an answer and the other half are for the explanation.