   Chapter 11.4, Problem 25E ### 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

# Allomelric relationships—fish For many species of fish, the allometric relationship between the weight W and the length L is approximately W = k L 3 , where k is a constant. Find the percent rate of change of the weight as a corresponding percent rate of change of the length.

To determine

To calculate: The percent rate of change of weight as a corresponding percent rate of change of the length if the allometric relationship between the weight W and the length L is approximately W=kL3.

Explanation

Given Information:

The allometric relationship between the weight W and the length L is approximately,

W=kL3.

Formula used:

The derivative formula,

ddxxn=nxn1

Calculation:

As it is provided that the allometric relationship between the weight W and the length L is approximately,

W=kL3.

Where k is a constant.

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

dWdt=ddt(kL3)=3kL2dLdt

Now, to obtain the percent rate of change of weight as corresponding percent rate of change of length, divide both sides by W to get,

dWdt=ddt(kL3

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