Question

For mammals, brain mass scales as body mass to the power of 0.70: Mbrain∝M0.70body.Mammal A has twice the body mass of mammal B. What is the ratio of mammal A's specific brain mass to mammal B's? Report your answer using two significant figures

Answer 1

The ratio of mammal A's specific brain mass to mammal B's can be calculated using the equation Mbrain∝M0.70body. Assuming mammal B's body mass is x, mammal A's body mass is 2x. Substituting these values, mammal A's specific brain mass is approximately 1.48 times that of mammal B.

Step-by-step explanation:

To find the ratio of mammal A's specific brain mass to mammal B's, we can use the equation Mbrain∝Mbody^0.70. Let's assume that mammal B's body mass is x. Therefore, mammal A's body mass is 2x. We can now substitute these values into the equation: (Mbrain_A/Mbrain_B) = (Mbody_A/Mbody_B)^0.70. Since mammal A has twice the body mass of mammal B, the ratio of their specific brain mass can be calculated as (2x/x)^0.70 = 2^0.70 = 1.48. Therefore, mammal A has approximately 1.48 times the specific brain mass of mammal B.

Answer 2

Ration of mammal A's specific brain mass to mammal B's
`= 1.624`

Step-by-step explanation:

Given -

Mass of brain is equal to 0.7th power of mass of body

Mass of brain in terms of mass of body of Mammal B

`= M^(0.7)`

Where M signifies the mass of body of mammal B

Mass of body of mammal A
`= 2*`mass of body of Mammal B
`= 2M`

Mass of brain of mammal A in terms of mass of body of Mammal B

`= 2M^(0.7)`

Ration of mammal A's specific brain mass to mammal B's

`((2M)^(0.7))/(M^(0.7)) \\= 2^(0.7)\\= 1.624`

Thus, Ration of mammal A's specific brain mass to mammal B's
`= 1.624`