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11 Nov 2019
A glucose solution is administered intravenously into the bloodstream of a patient m a hospital at a constant rate r. As the glucose is added, it is converted into other substances and removed from the bloodstream at a rate that is directly proportional to the concentration at that time. Thus, a model for the glucose solution concentration C = C(t)of the glucose solution in the bloodstream is where k is a positive constant. Suppose that the concentration at time t = 0 is C0. Determine a function for the concentration at any time t by solving the differential equation. Express your function for the concentration of the glucose in terms of r, k C0, and t. Assuming that C 0 k, find lim C(t) and write a short paragraph giving your interpretation of the results of the limit ,in terms of the patient in the hospital.
A glucose solution is administered intravenously into the bloodstream of a patient m a hospital at a constant rate r. As the glucose is added, it is converted into other substances and removed from the bloodstream at a rate that is directly proportional to the concentration at that time. Thus, a model for the glucose solution concentration C = C(t)of the glucose solution in the bloodstream is where k is a positive constant. Suppose that the concentration at time t = 0 is C0. Determine a function for the concentration at any time t by solving the differential equation. Express your function for the concentration of the glucose in terms of r, k C0, and t. Assuming that C 0 k, find lim C(t) and write a short paragraph giving your interpretation of the results of the limit ,in terms of the patient in the hospital.