A chain smoker smokes five cigarettes every hour. From each cigarette, 0.4 mg of nicotine is absorbed into the person’s bloodstream. Nicotine leaves the body at a rate proportional to the amount present, with constant of proportionality −0.346 if t is in hours.
(a) Write a differential equation for the level of nicotine in the body, N, in mg, as a function of time, t, in hours.
(b) Solve the differential equation from part (a). Initially there is no nicotine in the blood.
(c) The person wakes up at 7 am and begins smoking. How much nicotine is in the blood when the person goes to sleep at 11 pm (16 hours later)?