Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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6. A medication is administered to a patient. The amount, in milligrams, of the medication in the patient at dy 12- y time t hours is modeled by a function y = A (t) that satisfies the differential equation dt 3 t = 0 hours, there are 0 milligrams of the medication in the patient. (a) A portion of the slope field for the differential equation curve through the point (0, 0). ga y 1 1/ dy dt = with initial condition A(0) = 0. 12- y 3 | | || | || | || | || = is given below. Sketch the solution (b) Using correct units, interpret the statement lim A(t) = 12 in the context of this problem. tI8 At time (c) Use separation of variables to find y = A (t), the particular solution to the differential equation dy 12- y dt 3
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Transcribed Image Text:6. A medication is administered to a patient. The amount, in milligrams, of the medication in the patient at dy 12- y time t hours is modeled by a function y = A (t) that satisfies the differential equation dt 3 t = 0 hours, there are 0 milligrams of the medication in the patient. (a) A portion of the slope field for the differential equation curve through the point (0, 0). ga y 1 1/ dy dt = with initial condition A(0) = 0. 12- y 3 | | || | || | || | || = is given below. Sketch the solution (b) Using correct units, interpret the statement lim A(t) = 12 in the context of this problem. tI8 At time (c) Use separation of variables to find y = A (t), the particular solution to the differential equation dy 12- y dt 3
(d) A different procedure is used to administer the medication to a second patient. The amount, in milligrams, of the medication in the second patient at time t hours is modeled by a function y = B(t) that satisfies the At time t = 1 hour, there are 2.5 milligrams of the medication in y dy differential equation = 3 dt t+2 the second patient. Is the rate of change of the amount of medication in the second patient increasing or decreasing at time t = 1? Give a reason for your answer.
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Transcribed Image Text:(d) A different procedure is used to administer the medication to a second patient. The amount, in milligrams, of the medication in the second patient at time t hours is modeled by a function y = B(t) that satisfies the At time t = 1 hour, there are 2.5 milligrams of the medication in y dy differential equation = 3 dt t+2 the second patient. Is the rate of change of the amount of medication in the second patient increasing or decreasing at time t = 1? Give a reason for your answer.
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