Question #263616

The metabolic rate R ( kJ day^{-1}) of mammals varies with their body

mass M (kg) according to the power law R=k M^{3/4}. where k is a constant.

A common shrew has a mass of 9 g and a metabolic rate of 7 kJ day^{-1}.

(a) What is the metabolic rate in kJ day^{-1 }of a dog whose mass is 5 kg? Give the answer to at least 3 significant figures.

(b) What is the mass in kg of a cat with a metabolic rate 560 kJ day^{-1}? Give the answer to at least 3 significant figures.

Expert's answer

**a)Metabolic rate in kJ day**^{-1 }**of a dog whose mass is 5 kg;**

"=\\frac{5kg\\times 7KJday^{-1}}{9\\times10^{-3}Kg}"

=3,888.889 KJ day^{-1}

**b)mass in kg of a cat with a metabolic rate 560 kJ day**^{-1}

"=\\frac{560KJday^{-1}\\times 9\\times10^{-3}Kg}{7KJday^{-1}}"

=0.720 Kg

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