The popular sleep-aid drug Zaleplon has a half-life of one hour. That is, the amount of the drug present in the body is halved each hour. Suppose 10 mg of Zaleplon is taken at bedtime.
(a) Find the difference equation for yn, the amount of the drug present in the body after n hours.
(b) Solve the difference equation from part (a).
(c) Use the solution from part (b) to calculate the amount of the drug present in the body after 8 hours?