   Chapter 9.4, Problem 49E ### 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

# Metabolic rate According to Kleiber's law, the metabolic rate q of the vast majority of animals is related to the animals mass M according to q = k M 3 / 4 where k is a constant. This means that a cat, with mass about 100 times that of a mouse, has a metabolism about 100 3 / 4 ≈   32 times greater than that of a mouse. Find the function that describes the rate of change of the metabolic rate with respect to mass.

To determine

To calculate: The function that describes the rate of change of metabolic rate with respect to mass where the metabolic rate q is related to M according to the function q=kM34.

Explanation

Given Information:

The metabolic rate q is related to M according to the function q=kM34.

Formula Used:

According to power rule,

If f(x)=xn, then f(x)=nxn1.

Coefficient rule for a constant c is such that, if f(x)=cu(x), where u(x) is a differentiable function of x, then f(x)=cu(x).

Calculation:

Consider that the metabolic rate q is related to M according to the function q=kM34.

Rate of change of metabolic rate can be given by,

dqdM

Put q=kM34 to calculate the derivative as,

dqdM=d

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