High School

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In 2004, it was reported that "the relationship between body mass, [tex]M[/tex], and standard metabolic rate, [tex]B[/tex], among living organisms remains controversial. However, in many cases, [tex]B[/tex] is approximately proportional to the three-quarters power of [tex]M[/tex].

The average mass of an African forest elephant is 4.6 metric tons, and that of a typical mouse is 25 grams. Use this information to determine how many times greater the metabolic rate of an elephant is than that of a mouse. Recall that 1 metric ton = 1,000,000 grams.

Answer :

The answer is 8884.37 times

In many cases, B is approximately proportional to the three-quarters power of M:
[tex]B= M^{3/4} [/tex]

Elephant:
M1 = 4.6 mt = 4.6 * 1,000,000 g = 4,600,000 g
[tex]B1= 4600000^{3/4}=99327.24[/tex]

Mouse
M2 = 25 g
[tex]B2= 25^{3/4}=11.18[/tex]

determine how many times greater the metabolic rate of an elephant is than that of a mouse:
B1/B2 =
99327.24 / 11.18 = 8884.37 times

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