40. AMOUNT OF DRUG USAGE The amount, A, of anesthetics that a certain hospital uses each...

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40. 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. 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: dS dS dP dP dP dt dS dt dA dA dS dP' dS and- dA 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). 40. 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. 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: dS dS dP dP dP dt dS dt dA dA dS dP' dS and- dA 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).