Cephalexin is an antibiotic with a half-life in the body of

Question

Question: Cephalexin is an antibiotic with a half-life in the body of 0.9 hours, taken in tablets of 250 mg every six hours.

(a) What percentage of the cephalexin in the body at the start of a six-hour period is still there at the end (assuming no tablets are taken during that time)?

(b) Write an expression for Q₁, Q₂, Q₃, Q₄, where Qn mg is the amount of cephalexin in the body right after the nth tablet is taken.

(c) Express Q₃, Q₄ in closed form and evaluate them.

(d) Write an expression for Q_n and put it in closed form.

(e) If the patient keeps taking the tablets, use your answer to part (d) to find the quantity of cephalexin in the body in the long run, right after taking a tablet.