Consider an ordinary 100w incandescent light bulb and a led light bulb that produces the same amount of light, but consumes 20w of electricity. assuming the values for purchase price and lifetime for each bulb, and a cost of electricity as given below, compute the number of hours of usage required for the led light bulb to become more cost-effective than the incandescent bulb for each case below. if the crossover in cost occurs because a new bulb must be purchased, you may take the number of hours to be equal to the time at which the bulb must be purchased. note: one year of moderate usage corresponds to ~1000 hours

Because of the violent nature of the sport, professional american football players are at risk of suffering concussions (or brain injuries) during the violent collisions that occur between players during the game. violent collisions involving hits to the head are particularly risky. suppose the commissioner of the national football league (nfl) institutes a rule requiring players to wear a new, lighter helmet that is designed to reduce head trauma during collisions between players on the field. while the new helmets the probability of a concussion resulting from each individual collision, at the same time the new helmets could also give football players an incentive to play more , which could potentially the amount of violent collisions and thus the number of concussions suffered by nfl players, all else equal.