Chapter 3, Problem 40RE

Amount of Drug Usage The amount, $A$, of anesthetics that a certain hospital uses each week is a function of the number, $S$, of surgical operations performed each week. Also, $S$, in turn, is a function of the population, $P$, of the area served by the hospital, while $P$ is a function of time $t$.

Write the derivative symbols for the following quantities: (i) population growth rate; (ii) rate of change of anesthetic use with respect to population size; (iii) rate of change of surgical operations with respect to population size; (iv) rate of change of anesthetic use with respect to number of surgical operations. Select your answers from the following:

$\frac{dS}{dP},\frac{dS}{dt},\frac{dP}{dS},\frac{dP}{dt},\frac{dA}{dS},\frac{dA}{dP},$ and $\frac{dS}{dA}$.

Write a type of chain rule that expresses the time rate of change of anesthetic usange, $\frac{dA}{dt}$, in terms three of the derivatives described in part (a).