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A glucose solution is administered intravenously into the bloodstream 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 proportional to the concentration at that time. Thus a model for the concentration C = C(t) of the glucose solution in the bloodstream is
dC/dt = r - kC
where k is a positive constants.
(a) Suppose that the concentration at time t = 0 is C0.
Determine the concentration at any time t by solving the differential equation.
(b) Assuming that C0 < r/k, find limt→∞ C(t) and interpret your answer. |
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