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, for positive constant k, is: dC/dt =r−kC Explain that differential equation in words; what are the quantities, why are they subtracted, why in that order, etc... Then, suppose that the concentration at time t = 0 is C0. Determine the concentration at any time t by solving the differential equation. [Note - your solution will be in terms of C0]. Then, assuming that C0 < r/k, find lim C(t) and interpret what your answer means, in context. t→∞ (Show all steps plz)
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, for positive constant k, is:
dC/dt =r−kC
Explain that differential equation in words; what are the quantities, why are they subtracted, why in that order, etc... Then, suppose that the concentration at time t = 0 is C0. Determine the concentration at any time t by solving the differential equation. [Note - your solution will be in terms of C0]. Then, assuming that
C0 < r/k, find lim C(t) and interpret what your answer means, in context. t→∞ (Show all steps plz)
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