IF THE HALF-LIFE OF THE ANTI-BIOTIC IN THE BLOODSTREAM IS 3 HOURS, WHAT RATE OF INFUSION SHOULD HE PRESCRIBE TO MAINTAIN A LONG-TERM AMOUNT OF 400 MGS IN DIANA’S BLOODSTREAM?

IF THE HALF-LIFE OF THE ANTI-BIOTIC IN THE BLOODSTREAM IS 3 HOURS, WHAT RATE OF INFUSION SHOULD HE PRESCRIBE TO MAINTAIN A LONG-TERM AMOUNT OF 400 MGS IN DIANA’S BLOODSTREAM?

Diana is sick in hospital with a severe bacterial infection. she is to be fed antibiotics intravenously at a constant infusion rate, and the doctor knows that the anti-biotic will be eliminated from the bloodstream at a rate proportional to the amount y(t) present in the bloodstream at time t. if the half-life of the anti-biotic in the bloodstream is 3 hours, what rate of infusion should he prescribe to maintain a long-term amount of 400 mgs in diana’s bloodstream? 1. infusion rate = 1.694 mgs/min 2. infusion rate = 1.617 mgs/min 3. infusion rate = 1.848 mgs/min 4. infusion rate = 1.771 mgs/min 5. infusion rate = 1.54 mgs/min

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