Biologists have observed that the pulse rate P (in beats per minute) in animals

Question

Biologists have observed that the pulse rate P (in beats per minute) in animals is related to body mass (in kilograms) by the approximate formula

This is one of manyallometric scaling laws prevalent in biology. Is the absolute value

increasing or decreasing as m increases?????

Find the

for the animal whose weight is

kg.??????

Biologists have observed that the pulse rate P (in beats per minute) in animals is related to body mass (in kilograms) by the approximate formula P = 200m?1/4. This is one of manyallometric scaling laws prevalent in biology. Is the absolute value increasing or decreasing as m increases????? Find the for the animal whose weight is

Explanation / Answer

P = 200m^(-1/4)

dP/dm = 200 (-1/4) m^(-5/4)
dP/dm = -50m^(-5/4)

At m=32, dP/dm = -50 / 32^(5/4) = -0.65695

At m=32, P= 200/32^(1/4) = 84.0896

Equation of tangent line at (32, 84.0896) is:

P - 84.0896 = -0.65695 ( m - 32)
P = -0.65695m +84.0896+(32)(0.65695)
P= -0.65695m +105.112

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