Question

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

(a) Write a function that represents this relationship. If you must introduce a new variable, use k.

B=

The average mass of an African forest elephant is 4.7 metric tons, and that of a typical mouse is 27 grams. Use part (a) 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.

? times greater.

Answer 1

(a) Using k as the proportionality constant, the equation that can be generated from the given relationship is,
B = k(M^3/4)

(b) metabolic rate of the elephant
B = k(4.7 x 1,000,000)^(3/4) = 100942.35k
metabolic rate of the mouse
B = k(27)^(3/4) = 11.84k
Then, divide the metabolic rate of the elephant by the metabolic rate of the mouse,
n = 100942.35k/11.84k = 8522.18
Therefore, the metabolic rate of the elephant is approximately 8522.18 times that of the mouse.