An antibiotic is being administered intravenously to a patient. Fluid containing 4 mg/cm³ of the antibiotic enters the patient's bloodstream at a rate of 110 cm³/hour. The antibiotic is absorbed by the body or otherwise leaves the bloodstream at a rate proportional to the amount present, with a rate constant of 0.2 per hour. Assume the antibiotic is always uniformly distributed throughout the bloodstream. (i) Which of these is a differential equation for the amount of the antibiotic, A(t), in the bloodstream at any time t? O dA dt o da i dt O dA dt O dA dt = 440A(t) 0.2 2200 = 440 - 0.2A(t) = 440A(1) (ii) How much of the antibiotic is present in the bloodstream after a very long time? Round your answer to the nearest hundredth of a milligram. = -0.2A(t) mg eTextbook and Media (iii) What is the general solution of the differential equation in (i)? © A(t) = – 440 + Ke02t 1 A(t) = 2.20E+3 ⒸA(t) = 440+ Ke-0.21 ⒸA(1) = 2.20E+3+ Ke-0.2r ⒸA(1) = 2.20E+3+ Ke.21 + Ke-0.21

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