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A.) In 2004, it was reported that "the relationship between body mass, \( M \), and standard metabolic rate, \( B \), 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 \( k \).

\[ B = kM^{3/4} \]

B.) The average mass of an African forest elephant is 4.7 metric tons, and that of a typical mouse is 25 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 :

Final answer:

The relationship between MM and BB can be expressed as B = k*(M^3/4). To find the metabolic rate of an elephant to a mouse, convert the mass to the same units, cancel out the common constant k, and calculate the ratio.

Explanation:

The relationship between the body mass, MM, and standard metabolic rate, BB, can be represented as follows:

B = k * (M^3/4)

where k is a constant. The exact value of k would depend on the units used for mass and metabolic rate.

To compute the metabolic rate of the elephant and the mouse, recall that 1 metric ton equals 1,000,000 grams.

So, the mass of an elephant in grams is 4.7 * 1,000,000 = 4,700,000 grams and the mass of a mouse is 25 grams. Hence, the ratio of their metabolic rate is given by:

(k * (4,700,000^3/4)) / (k * (25^3/4))

The k variable, being a common factor, cancels out themselves.

Therefore, we would get:

4,700,000^3/4 / 25^3/4

By calculating this expression you get the ratio of metabolic rates, which is the number of times the metabolic rate of an elephant is than that of a mouse.

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Rewritten by : Barada

A )
The equation of relationship is:
B = k · M ^(3/4)
B )
4.7 tons = 4,700,000 g
B ( mouse ) = k · 25 ^(3/4)
B ( elephant) = k · 4,700,000 ^(3/4)
B ( el ) / B ( m ) = k · 4,700,000 ^(3/4) / k · 25^(3/4) =
= ( 4,700,000 / 25 )^(3/4) = 188,000^(3/4) = 9,029 times