Chapter 7.8, Problem 61ES

Medication can be administered to a patient using a variety of methods. For a given method, let c(t) denote the concentration of medication in the patient’s bloodstream (measures in mg/L) t hours after the dose is given. The area under the curve $c=c\left(t\right)$ over the time interval $[0,+\infty )$ indicates the “availability� of the medication for the patient’s body. Determine which method provides the greater availability.

$\begin{array}{l}\text{Method}1:c_1(t)=5(e^{-0.2t}-e^{-t});\\ \text{Method}2:c_2(t)=4(e^{-0.2t}-e^{-3t});\end{array}$