Explanation Approach: The logarithmic function, log b x = a if and only if x = b a . Given: The relation between the stand-density index SDI, the number N of trees per acre, and the diameter D , in inches, of a tree per acre, and the diameter D , in inches, of a tree of average size. This ingredient is an empirical relationship between N and D for fully stocked stands -that is, stands for which the tree density is in some sense optimal for the given size of the trees. This relationship, which was observed by L.H.R eineke in 1933 , is log N = − 1.605 log D + k Where k is a constant that depends on the species in question. Calculation: The given model is, log N = − 1 To determine (b) To find: The effect of multiplying the average size of a tree by a factor of 2 has on the number of trees per acre. To determine (c) To find: The effect on N on increasing the constant by 1 and if D remains same.

6th Edition

ISBN: 9780357422496

Author: Crauder

Publisher: CENGAGE L

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Question

Chapter 4.5, Problem 18E

To determine

(a)

To find:

The number of trees per acre when the constant k is 4.1 and the diameter of a tree of average size is 8 inches.

To determine

(b)

To find:

The effect of multiplying the average size of a tree by a factor of 2 has on the number of trees per acre.

To determine

(c)

To find:

The effect on N on increasing the constant by 1 and if D remains same.

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Chapter 4.5, Problem 17E

Chapter 4.5, Problem 19E

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Chapter 4 Solutions

FUNCTIONS+CHANGE -WEBASSIGN

Ch. 4.1 - TEST YOUR UNDESTANDING| FOR EXAMPLE 4.1...Ch. 4.1 - TEST YOUR UNDERSTANDING| FOR EXAMPLE 4.2 In a...Ch. 4.1 - Prob. 3TU Ch. 4.1 - Reminder Round all answers to two decimal places...Ch. 4.1 - Reminder Round all answers to two decimal places...Ch. 4.1 - Reminder Round all answers to two decimal places...Ch. 4.1 - Reminder Round all answers to two decimal places...Ch. 4.1 - Reminder Round all answers to two decimal places...Ch. 4.1 - Reminder Round all answers to two decimal places...Ch. 4.1 - Reminder Round all answers to two decimal places...

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(a) To find: The number of trees per acre when the constant k is 4.1 and the diameter of a tree of average size is 8 inches.

Solution Summary: The author analyzes the relationship between the stand-density index SDI, the number N of trees per acre, and the diameter D for fully stocked stands.

(a) To find: The number of trees per acre when the constant k is 4.1 and the diameter of a tree of average size is 8 inches.

(b) To find: The effect of multiplying the average size of a tree by a factor of 2 has on the number of trees per acre.

(c) To find: The effect on N on increasing the constant by 1 and if D remains same.

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Chapter 4 Solutions

(a)

To find:

The number of trees per acre when the constant k is 4.1 and the diameter of a tree of average size is 8 inches.

(b)

To find:

The effect of multiplying the average size of a tree by a factor of 2 has on the number of trees per acre.

(c)

To find:

The effect on N on increasing the constant by 1 and if D remains same.