# [Get Answer] Evaluate ymax and ymin by examining one time period between pills.

If antiMegatherium the medicine against giant sloth is administered intravenously at a steady rate Show more If antiMegatherium the medicine against giant sloth is administered intravenously at a steady rate of q mg per day then the total amount of the drug in the patients body at time t in days x(t) mg satisfies the differential equation x + kx = q; x(0) = 0 (k > 0). (a) (Sep 11 10 pts): Find x(t) and find k supposing that when a patient receives a constant dose of q = 40 mg per day x(t ) 20 mg. Be sure to specify the units of k. (b) (Sep 11 6 pts): Suppose instead that the patient takes 4 pills of 10 mg each per day equally spaced. Denote by y(t) the total amount of the drug in the body. Make a qualitative sketch of the graph of the function y(t) for 24 hours assuming that we are in the steady state situation in which each successive period of 6 hours looks the same as the others. Label on the vertical axis the maximum and minimum levels of the drug in the body ymax and ymin. Draw a vertical segment to designate the jump in y each time the patient takes a pill. c) (Sep 11 10 pts): Its more convenient to take a pill than to receive a drug intravenously but the amount of the drug in the body varies more. Find out by how much in this problem. Evaluate ymax and ymin by examining one time period between pills. (You can compare these values to the baseline value of 20 mg.) Show less