Cup of coffee contains about 100 mg. of caffeine and leaves the body at a continuous of13% per hour. the function 100e gives the amount of caffeine (in mg) remaining in the body t hours after drinking a cup of coffee. a) identify the vertical intercept of this function. write it as an ordered pair. in a complete a) sentence, interpret its meaning in the context of this situation. b) how much caffeine remains in the body 8 hours after drinking a cup of coffee? (round to two decimal places, as needed) c) how long will it take the body to metabolize half of the caffeine from one 8-oz cup coffee? (that is, how long until only 50 mg. of caffeine remain in the body? ) show all your work and write your answer in a complete sentence. give answers in exact form and approximate form, rounded to two decimal places. d) according to this model, is it possible for all of the caffeine to leave the body? explain.