Question

A study finds that the metabolic rate of mammals is proportional to m^3/4 , where m is the total body mass. By what factor does the metabolic rate of a 70.0-kg human exceed that of a 4.91-kg cat?

Answer 1

To determine the factor by which a human's metabolic rate exceeds that of a cat, the formula MR ≈ m^{3/4} is used. By calculating (70.0 kg)^{3/4} ÷ (4.91 kg)^{3/4}, the result is a unitless number indicating the factor difference.

Step-by-step explanation:

To find by what factor the metabolic rate of a 70.0-kg human exceeds that of a 4.91-kg cat, given that the metabolic rate (MR) is proportional to the body mass (m) raised to the power of 3/4, we can use the formula:

MR ≈ m^{3/4}

For the human, MR_human ≈ (70.0 kg)^{3/4} and for the cat, MR_cat ≈ (4.91 kg)^{3/4}. To find the factor by which the human's MR exceeds the cat's, you divide the human's MR by the cat's MR:

Factor = ÷ MR_human/MR_cat

Calculating this gives us:

Factor = (70.0 kg)^{3/4} ÷ (4.91 kg)^{3/4}

After computing the values, you arrive at the factor by which a human's metabolic rate is higher than that of a cat. Note that the units of kilograms cancel out, so the factor is a unitless number.

Answer 2

The mass of human is 2898 times of the mass of cat.

Step-by-step explanation:

A study finds that the metabolic rate of mammals is proportional to m^3/4 i.e.

`M=(km^3)/(4)`

Where

k is constant

If m = 70 kg, the mass of human

`M=(70^3)/(4)\\\\=85750`

If m = 4.91 kg, the mass of cat

`M'=(4.91^3)/(4)\\\\=29.59`

So,

`(M)/(M')=(85750)/(29.59)\\\\=2897.93\approx 2898`

So, the mass of human is 2898 times of the mass of cat.