5. The amount of caffeine metabolised by the human body can be modelled by the formula, C(t) = 120e t where C(t) (in milligrams, mg) is the concentration of caffeine in the blood-stream t hours after the coffee has been drunk. The value 120 in the formula, refers to the initial amount of caffeine ingested by the consumer in mg. (i) If it takes 5 hours for half of the initial caffeine ingested to remain in the body, according to this model, what is the value of k. You will need to use a logarithm rule to make k the subject of your calculation. [3 marks] (ii) How long will it take for C(t) = 20mg? [3 marks]