Suppose the average daily metabolic rate for certain types of animals can be exp

Question

Suppose the average daily metabolic rate for certain types of animals can be expressed as a function of mass by r = 121.6m 0.75, where m is the mass of the animal (in kilograms) and r is the metabolic rate (in kcal per day). If the mass of an animal is changing at a rate of dm/dt, find dr/dt. Determine dr/dt for a 210-kg animal that is gaining mass at a rate of 3 kg per day. If the mass of an animal is changing at a rate of dm/dt, find dr/dt. Determine dr/dt for a 210-kg animal that is gaining mass at a rate of 3 kg per day. For the animal described, dr/dt = kcal per day, each day. (Round to the nearest thousandth as needed.)

Explanation / Answer

a)r = 121.6*m^0.75 =>dr/dt = 121.6*0.75*m^0.75-1*dm/dt = 91.2/m^0.25 * dm/dt b)m = 210, dm/dt = 3 kg/day =>dr/dt = (91.2/(210^0.25))*3 = 71.872

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