The half-life of caffeine in a healthy adult's bloodstream is 5.7 hours. Suppose Alex, a healthy adult, drinks a Grande Latte, which contains 150 mg of caffeine, at 4 p.m. (assume, perhaps unrealistically, all of the caffeine absorbed into Alex's bloodstream immediately). Use the exponential decay model A(t) = A e where t is the time since 4 p.m. measured in hours and A(t) is the amount of caffeine in Alex's bloodstream at time t. a) Find the exponential decay rate, k, for the caffeine in Alex's bloodstream. (Express your answer as a percentage rounded to two decimal places.) (2 points) b) At what time of the night will there be only 50 mg of caffeine in Alex's bloodstream? (State your answer as the time rounded to the nearest minute). (2 points)