Business Calculus Quiz
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DIFFERENTIAL EQUATIONS (BUSINESS MODELS)
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A pharmaceutical company models drug concentration in blood using dCdt=−kC+R\frac{dC}{dt} = -kC + R where C(t)C(t) is concentration (mg/L), k=0.3 hr−1k = 0.3 \text{ hr}^{-1}, and R=12 mg/L/hrR = 12 \text{ mg/L/hr} is the infusion rate. The solution is C(t)=Rk+(C0−Rk)e−ktC(t) = \frac{R}{k} + \left(C_0 - \frac{R}{k}\right)e^{-kt}. If steady-state concentration must not exceed 45 mg/L for safety, and the patient starts with zero drug concentration, after how many hours will the concentration first reach 95% of steady-state?
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