Chapter 13.1, Problem 9ES

Suppose that the concentration C in mg/L of medication in a patient's bloodstream is modelled by the function $C\left(x,t\right)=0.2x\left(e^{-0.2t}-e^{-t}\right),$ where x is the dosage of the medication in mg and t is the number of hours since the beginning of administration of the medication.

(a) Estimate the value of $C\left(25,3\right)$ to two decimal places. Include appropriate units and interpret your answer in a physical context.

(b) If the dosage is 100 mg, give a formula for the concentration as a function of time t.

(c) Give a formula that describes the concentration after 1 hour in terms of the dosage x.