Patients undergo dialysis treatment to remove urea from their blood when their kidneys are not functioning properly.

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Patients undergo dialysis treatment to remove urea from their blood when their kidneys are not functioning properly. Blood is diverted from the patient through a machine that filters out urea. Under certain conditions, the duration of dialysis required, given that the initial urea concentration is c > 1, is given by the equation

3c + 9c2 – 8c t = In

Calculate the derivative of t with respect to c and interpret it.

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