   Chapter 3.1, Problem 52E ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

#### Solutions

Chapter
Section ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

# The number of tree species S in a given area A in the Pasoh Forest Reserve in Malaysia has been modeled by the power functionS(A) = 0.882A0.842where A is measured in square meters. Find S'(100) and interpret your answer.Source: Adapted from K. Kochummen et al., “Floristic Composition of Pasoh Forest Reserve, A Lowland Rain Forest in Peninsular Malaysia,” Journal of Tropical Forest Science (1991):1–13.

To determine

To find: The value of S(100) and interpret the result.

Explanation

Given:

The number of tree species S in area A is S(A)=0.882A0.842, where A is measured in square meters.

Derivative rules:

Power Rule: ddx(xn)=nxn1

Calculation:

Obtain the derivative of S(A) with respect to A.

S(A)=dSdA=ddA(0.882A0.842)

=0.882ddA(A0.842)

Apply the power rule and simplify the terms,

S(A)=0.882(0.842A0.8421)=(0.882)(0

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