   Chapter 11.4, Problem 27E ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

#### Solutions

Chapter
Section ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# Allometric relationships—crabs For fiddler crabs, data gathered by Thompson* show that the allometric relationship between the weight C of the claw and the weight VV of the body is given by C   =   0.11 W − 1.54 Find the percent rate of change of the claw weight in terms of the percent rate of change of the body weight for fiddler crabs.

To determine

To calculate: The percent rate of change of resistance of a claw weight in terms of the percent rate of change of the body weight for fiddler crabs if the allometric relationship between the weight C of the claw and the weight W of the body is given by C=0.11W1.54.

Explanation

Given Information:

The allometric relationship between the weight C of the claw and the weight W of the body is given by,

C=0.11W1.54

Formula used:

The derivative formula,

ddxxn=nxn1

Calculation:

As it is provided that the allometric relationship between the weight C of the claw and the weight W of the body is given by,

C=0.11W1.54.

To obtain the rate of change of weight of claw, differentiate above equation with respect to t as,

dCdt=1.54(0.11W0.54)dWdt=0.1694W0.54dWdt

Now, to obtain the percent rate of change of claw weight as corresponding percent rate of change of body weight, divide both sides by C to get,

dCdtC=0

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