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.

(a) 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:

(b) Write a type of chain rule that expresses the time rate of change of anesthetic usage, dA/dt, in terms of three of the derivatives described in part (a).

Transcribed Image Text:

ds ds dP dp dP' dt' ds' ds' dt VP VP ds' dp' and SP dA