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.

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

6th Edition

ISBN: 9781337515610

Author: Crauder

Publisher: Cengage

See similar textbooks

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.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 4.5, Problem 17E

Chapter 4.5, Problem 19E

Students have asked these similar questions

The spotted lanternfly, Lycorma delicatula, is an invasive species to the United States that has the potential to do significant agricultural damage. An ecologist is studying the relationship between the size of the female spotted lanternflies and the number of eggs they produce. The data are summarized below. Length of insect: AVG = 1 inch, SD = 0.15 inchNumber of eggs: AVG = 40 eggs, SD = 5 eggsr = 0.2 Using regression, we can say that the average number of eggs produced by female spotted lanternflies who are 1.1 inch long is closest to... Group of answer choices 42 39 40 41

Turbid water is muddy or cloudy water. Sunlight is necessary for most life forms; thus turbid water is considered a threat to wetland ecosystems. Passive filtration systems are commonly used to reduce turbidity in wetlands. Suspended solids are measured in mg/l. Is there a relation between input and output turbidity for a passive filtration system and, if so, is it statistically significant? At a wetlands environment in Illinois, the inlet and outlet turbidity of a passive filtration system have been measured. A random sample of measurements are shown below. (Reference: EPA Wetland Case Studies.) Reading Inlet (mg/l) Outlet (mg/l) 3 4 5 6 7 8 9 10 11 12 31.6 86.9 87.0 12.0 45.4 43.3 32.3 77.7 71.7 85.9 64.9 80.1 3.3 14.2 16.8 5.7 4.6 6.2 3.4 7.7 8.0 7.4 8.7 14.3 Use a 1% level of significance to test the claim that there is a monotone relationship (either way) between the ranks of the inlet readings and outlet readings. (a) Rank-order the inlet readings using 1 as the largest data…

Turbid water is muddy or cloudy water. Sunlight is necessary for most life forms; thus turbid water is considered a threat to wetland ecosystems. Passive filtration systems are commonly used to reduce turbidity in wetlands. Suspended solids are measured in mg/l. Is there a relation between input and output turbidity for a passive filtration system and, if so, is it statistically significant? At a wetlands environment in Illinois, the inlet and outlet turbidity of a passive filtration system have been measured. A random sample of measurements are shown below. (Reference: EPA Wetland Case Studies.) Reading 1 2 3 4 5 6 7 8 9 10 11 12 Inlet (mg/l) 59.1 25.7 70.5 71.0 37.6 43.5 13.1 24.2 16.7 49.1 67.6 31.7 Outlet (mg/l) 18.2 14.3 15.3 17.5 13.1 8.0 4.1 4.4 4.3 5.8 16.3 7.1 Use a 1% level of significance to test the claim that there is a monotone relationship (either way) between the ranks of the inlet readings and outlet readings. (a) Rank-order the inlet readings using 1 as…

Chapter 4 Solutions

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

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...

Knowledge Booster

(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.

Want to see the full answer?

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.