Find the function that gives the rate of change of claw weight with respect to body weight.

Question

Data for fiddler crabs analyzed by a company show that the allometric relationship between the weight C of the claw and the weight W of the body is given by

C = 0.17W^1.24.

Find the function that gives the rate of change of claw weight with respect to body weight. (Use exact numerical values. Do not round.)

dC/dw = ?

Answer 1

If this equation stated C = 5W^2, you would determine dC/dw by the power rule or dc/dw = 10w. The problem is no different because the power rule states that if f(x) = cx^n, then f/(x) = ncx^(n-1). We apply the power rule to determine:

dC/dw = 0.17(1.24)W^0.24

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