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Concentration of Glucose in the Bloodstream A glucose solution is administered intravenously into the bloodstream at a constant rate of r mg/hr. As the glucose is being administered, it is converted into other substances and removed from the bloodstream. Suppose the concentration of the glucose solution at time t is given by
where C0 is the concentration at time t = 0 and k is a positive constant. Assuming that C0 < r/k, evaluate
- a. What does your result say about the concentration of the glucose solution in the long run?
- b. Show that the function C is increasing on (0, ∞).
- c. Show that the graph of C is concave downward on (0, ∞).
- d. Sketch the graph of the function C.
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Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach
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