Chapter 5.9, Problem 59ES

Medication can be administered to a patient in different ways. For a given method, let $c\left(t\right)$ denote the concentration of medication in the patient’s bloodstream (measured in $\text{mg/L}$ ) $t$ hours after the dose is given. Over the time interval $0\le t\le b$ , the area between the graph of $c=c\left(t\right)$ and the interval $\left[0,b\right]$ indicates the “availability� of the medication for the patient’s body over that time period. Determine which method provides the greater availability over the given interval.

Method 1: $c\left(t\right)=5.78\left(e^{-0.4t}-e^{-1.3t}\right),$

Method 2: $c\left(t\right)=4.15\left(e^{-0.4t}-e^{-3t}\right);\left[0,4\right]$