11th Edition

ISBN: 9780321979438

Author: Margaret L. Lial, Raymond N. Greenwell, Nathan P. Ritchey

Publisher: PEARSON

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Textbook Question

Chapter 2.4, Problem 56E

Northern Spotted Owl Population In an attempt to save the endangered northern spotted owl, the U.S, Fish and Wildlife Service imposed strict guidelines for the use of 12 million acres of Pacific Northwest forest. This decision led to a national debate between the logging industry and environmentalists. Mathematical ecologists have created a mathematical model to analyze population dynamics of the northern spotted owl by dividing the female owl population into three categories: juvenile (up to 1 year old), subadult (1 to 2 years), and adult (over 2 years old). By analyzing these three subgroups, it is possible to use the number of females in each subgroup at time n to estimate the number of females in each group at any time n + 1 with the following matrix equation:

[ j n + 1 s n + 1 a n + 1 ] = [ 0 0 0.33 0.18 0 0 0 0.71 0.94 ] [ j n s n a n ] ,

where j_n is the number of juveniles, s_n is the number of sub-adults, and a_n is the number of adults at time n. Source: Conservation Biology.

(a) If there are currently 4000 female northern spotted owls made up of 900 juveniles, 500 subadults, and 2600 adults, use a graphing calculator or spreadsheet and matrix operations to determine the total number of female owls for each of the next 5 years. (Hint: Round each answer to the nearest whole number after each matrix multiplication.)

Chapter 2.4, Problem 56E, 56. Northern Spotted Owl Population In an attempt to save the endangered northern spotted owl, the

(b) With advanced techniques from linear algebra, it is possible to show that in the long run, the following holds.

[ j n + 1 s n + 1 a n + 1 ] ≈ 0.98359 [ j n s n a n ]

What can we conclude about the long-term survival of the northern spotted owl?

(c) Notice that only 18 percent of the juveniles become sub-adults. Assuming that, through better habitat management, this number could be increased to 40 percent, rework part (a). Discuss possible reasons why only 18 percent of the juveniles become subadults. Under the new assumption, what can you conclude about the long-term survival of the northern spotted owl?

Branch of mathematics concerned with mathematical structures that are closed under operations like addition and scalar multiplication. It is the study of linear combinations, vector spaces, lines and planes, and some mappings that are used to perform linear transformations. Linear algebra also includes vectors, matrices, and linear functions. It has many applications from mathematical physics to modern algebra and coding theory.

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Chapter 2.4, Problem 55E

Chapter 2.4, Problem 57E

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Chapter 2 Solutions

Finite Mathematics (11th Edition)

Ch. 2.1 - Use the echelon method to solve each system of two...Ch. 2.1 - Use the echelon method to solve each system of two...Ch. 2.1 - Use the echelon method to solve each system of...Ch. 2.1 - Use the echelon method to solve each system of two...Ch. 2.1 - Prob. 5E Ch. 2.1 - Prob. 6E Ch. 2.1 - Prob. 7E Ch. 2.1 - Use the echelon method to solve each system of...Ch. 2.1 - Prob. 9E Ch. 2.1 - Prob. 10E

Ch. 2.1 - Use the echelon method to solve each system of...Ch. 2.1 - Use the echelon method to solve each system of two...Ch. 2.1 - Use the echelon method to solve each system of two...Ch. 2.1 - Use the echelon method to solve each system of two...Ch. 2.1 - Prob. 15E Ch. 2.1 - Use the echelon method to solve each system of two...Ch. 2.1 - Prob. 17E Ch. 2.1 - Use the echelon method to solve each system of two...Ch. 2.1 - Use the echelon method to solve each system of two...Ch. 2.1 - Prob. 20E Ch. 2.1 - An inconsistent system...Ch. 2.1 - Prob. 22E Ch. 2.1 - Describe what a parameter is arid why it is used...Ch. 2.1 - In your own words, describe the echelon method as...Ch. 2.1 - Prob. 25E Ch. 2.1 - Solve each system of equations. Let z be the...Ch. 2.1 - Solve each system of equations. Let z be the...Ch. 2.1 - Prob. 28E Ch. 2.1 - Prob. 29E Ch. 2.1 - For each of the following systems of equations in...Ch. 2.1 - For each of the following systems of equations in...Ch. 2.1 - Prob. 32E Ch. 2.1 - Prob. 33E Ch. 2.1 - Prob. 34E Ch. 2.1 - Groceries If 20 lb of rice and 10 lb of potatoes...Ch. 2.1 - 36. Downloads Blake Allvine spent $35.97...Ch. 2.1 - Prob. 37E Ch. 2.1 - 38. Sales An apparel shop sells skirts for $45...Ch. 2.1 - Prob. 39E Ch. 2.1 - 40. Stock Lorri Morgan has $16,000 invested in...Ch. 2.1 - Banking A bank teller has a total of 70 bills in...Ch. 2.1 - Rug Cleaning Machines Kelly Karpet Kleaners sells...Ch. 2.1 - Prob. 43E Ch. 2.1 - Prob. 44E Ch. 2.1 - Prob. 45E Ch. 2.1 - Prob. 46E Ch. 2.1 - Prob. 47E Ch. 2.1 - 48. Flight Time A flight leaves New York at 8...Ch. 2.1 - 49. The 24® Game The object of the 24 Game,...Ch. 2.2 - Write the augmented matrix fur each system. Do...Ch. 2.2 - Write the augmented matrix for each system. Do...Ch. 2.2 - Prob. 3E Ch. 2.2 - Prob. 4E Ch. 2.2 - Prob. 5E Ch. 2.2 - Prob. 6E Ch. 2.2 - Write the system of equations associated with...Ch. 2.2 - Prob. 8E Ch. 2.2 - Prob. 9E Ch. 2.2 - Prob. 10E Ch. 2.2 - Prob. 11E Ch. 2.2 - Use the indicated row operations to change each...Ch. 2.2 - Prob. 13E Ch. 2.2 - Prob. 14E Ch. 2.2 - Prob. 15E Ch. 2.2 - Prob. 16E Ch. 2.2 - Prob. 17E Ch. 2.2 - Prob. 18E Ch. 2.2 - Prob. 19E Ch. 2.2 - Prob. 20E Ch. 2.2 - Use the Gauss-Jordan method to solve each system...Ch. 2.2 - Use the Gauss-Jordan method to solve each system...Ch. 2.2 - Prob. 23E Ch. 2.2 - Prob. 24E Ch. 2.2 - Prob. 25E Ch. 2.2 - Use the Gauss-Jordan method to solve each system...Ch. 2.2 - Prob. 27E Ch. 2.2 - Use the Gauss-Jordan method to solve each system...Ch. 2.2 - Prob. 29E Ch. 2.2 - Prob. 30E Ch. 2.2 - Prob. 31E Ch. 2.2 - Prob. 32E Ch. 2.2 - Prob. 33E Ch. 2.2 - Prob. 34E Ch. 2.2 - Prob. 35E Ch. 2.2 - Prob. 36E Ch. 2.2 - Prob. 37E Ch. 2.2 - Prob. 38E Ch. 2.2 - Prob. 39E Ch. 2.2 - Prob. 40E Ch. 2.2 - Prob. 41E Ch. 2.2 - Prob. 42E Ch. 2.2 - 43. On National Public Radio, the "Weekend...Ch. 2.2 - Prob. 44E Ch. 2.2 - Investments Katherine Chong invests $10,000...Ch. 2.2 - 46. Office Technology Pyro-Tech, Inc. is...Ch. 2.2 - Prob. 47E Ch. 2.2 - Prob. 48E Ch. 2.2 - Loans To get the necessary funds for a planned...Ch. 2.2 - Manufacturing Nadir, Inc. produces three models of...Ch. 2.2 - 51. Deliveries An electronics company produces...Ch. 2.2 - Tents L.L. Bean makes three sizes of Ultra Dome...Ch. 2.2 - Transportation A manufacturer purchases a part for...Ch. 2.2 - APPLY IT Transportation An auto manufacturer sends...Ch. 2.2 - Prob. 55E Ch. 2.2 - 56. Packaging A company produces four...Ch. 2.2 - Prob. 57E Ch. 2.2 - Animal Breeding An animal breeder can buy four...Ch. 2.2 - Prob. 59E Ch. 2.2 - Prob. 60E Ch. 2.2 - Prob. 61E Ch. 2.2 - Prob. 62E Ch. 2.2 - Prob. 63E Ch. 2.2 - Prob. 64E Ch. 2.2 - 65. Modeling War One of the factors that...Ch. 2.2 - Prob. 66E Ch. 2.2 - 67. Baseball Ichiro Suzuki holds the American...Ch. 2.2 - Prob. 68E Ch. 2.2 - 69. Toys One hundred toys are to be given out to...Ch. 2.2 - Prob. 70E Ch. 2.2 - Prob. 71E Ch. 2.2 - Prob. 72E Ch. 2.2 - Prob. 73E Ch. 2.3 - Prob. 1E Ch. 2.3 - Prob. 2E Ch. 2.3 - Prob. 3E Ch. 2.3 - Prob. 4E Ch. 2.3 - Decide whether each statement is true or false. If...Ch. 2.3 - Prob. 6E Ch. 2.3 - Prob. 7E Ch. 2.3 - Prob. 8E Ch. 2.3 - Prob. 9E Ch. 2.3 - Prob. 10E Ch. 2.3 - Prob. 11E Ch. 2.3 - Prob. 12E Ch. 2.3 - Prob. 13E Ch. 2.3 - Prob. 14E Ch. 2.3 - Prob. 15E Ch. 2.3 - Prob. 16E Ch. 2.3 - Prob. 17E Ch. 2.3 - Prob. 18E Ch. 2.3 - Prob. 19E Ch. 2.3 - Prob. 20E Ch. 2.3 - Prob. 21E Ch. 2.3 - Prob. 22E Ch. 2.3 - Prob. 23E Ch. 2.3 - Prob. 24E Ch. 2.3 - Prob. 25E Ch. 2.3 - Prob. 26E Ch. 2.3 - Prob. 27E Ch. 2.3 - Prob. 28E Ch. 2.3 - Prob. 29E Ch. 2.3 - Prob. 30E Ch. 2.3 - Prob. 31E Ch. 2.3 - Prob. 32E Ch. 2.3 - For matrices X=[ xyzw] and 0=[ 0000], find the...Ch. 2.3 - Prob. 34E Ch. 2.3 - Prob. 35E Ch. 2.3 - Prob. 36E Ch. 2.3 - Prob. 37E Ch. 2.3 - Prob. 38E Ch. 2.3 - Prob. 39E Ch. 2.3 - Prob. 40E Ch. 2.3 - Prob. 41E Ch. 2.3 - 42. Trading Partners The table below gives, the...Ch. 2.3 - Prob. 43E Ch. 2.3 - Prob. 44E Ch. 2.3 - Testing Medication A drug company is testing 200...Ch. 2.3 - Prob. 46E Ch. 2.3 - Prob. 47E Ch. 2.3 - Prob. 48E Ch. 2.3 - Prob. 49E Ch. 2.3 - Prob. 50E Ch. 2.4 - Let A=[ -2-403] and B=[ -6240]. Find each value....Ch. 2.4 - Prob. 2E Ch. 2.4 - Prob. 3E Ch. 2.4 - Prob. 4E Ch. 2.4 - Prob. 5E Ch. 2.4 - Let and Find each value. 6. 7B– 3A Ch. 2.4 - Prob. 7E Ch. 2.4 - Prob. 8E Ch. 2.4 - Prob. 9E Ch. 2.4 - Prob. 10E Ch. 2.4 - Prob. 11E Ch. 2.4 - Prob. 12E Ch. 2.4 - To find the product matrix AB, the number of...Ch. 2.4 - Prob. 14E Ch. 2.4 - Prob. 15E Ch. 2.4 - Prob. 16E Ch. 2.4 - Prob. 17E Ch. 2.4 - Prob. 18E Ch. 2.4 - Find each matrix product, if possible. 19. Ch. 2.4 - Find each matrix product, if possible. [...Ch. 2.4 - Prob. 21E Ch. 2.4 - Prob. 22E Ch. 2.4 - Prob. 23E Ch. 2.4 - Prob. 24E Ch. 2.4 - Prob. 25E Ch. 2.4 - Prob. 26E Ch. 2.4 - Prob. 27E Ch. 2.4 - Prob. 28E Ch. 2.4 - Prob. 29E Ch. 2.4 - Prob. 30E Ch. 2.4 - Prob. 31E Ch. 2.4 - Prob. 32E Ch. 2.4 - Prob. 33E Ch. 2.4 - Prob. 34E Ch. 2.4 - Prob. 35E Ch. 2.4 - Prob. 36E Ch. 2.4 - Given matrices verify that the statements in...Ch. 2.4 - Prob. 38E Ch. 2.4 - Prob. 39E Ch. 2.4 - Prob. 40E Ch. 2.4 - Prob. 41E Ch. 2.4 - Prob. 42E Ch. 2.4 - Use a computer or graphing calculator arid the...Ch. 2.4 - Prob. 44E Ch. 2.4 - Prob. 45E Ch. 2.4 - Prob. 46E Ch. 2.4 - Prob. 47E Ch. 2.4 - Prob. 48E Ch. 2.4 - Prob. 49E Ch. 2.4 - Prob. 50E Ch. 2.4 - Prob. 51E Ch. 2.4 - Prob. 52E Ch. 2.4 - Prob. 53E Ch. 2.4 - Prob. 54E Ch. 2.4 - Prob. 55E Ch. 2.4 - 56. Northern Spotted Owl Population In an attempt...Ch. 2.4 - 57. World Population The 2010 birth and death...Ch. 2.5 - Prob. 1E Ch. 2.5 - Decide whether the given matrices are inverses...Ch. 2.5 - Prob. 3E Ch. 2.5 - Decide whether the given matrices are inverses of...Ch. 2.5 - Decide whether the given matrices are inverses of...Ch. 2.5 - Prob. 6E Ch. 2.5 - Prob. 7E Ch. 2.5 - Prob. 8E Ch. 2.5 - Prob. 9E Ch. 2.5 - Prob. 10E Ch. 2.5 - Prob. 11E Ch. 2.5 - Prob. 12E Ch. 2.5 - Prob. 13E Ch. 2.5 - Prob. 14E Ch. 2.5 - Prob. 15E Ch. 2.5 - Prob. 16E Ch. 2.5 - Prob. 17E Ch. 2.5 - Prob. 18E Ch. 2.5 - Prob. 19E Ch. 2.5 - Prob. 20E Ch. 2.5 - Prob. 21E Ch. 2.5 - Prob. 22E Ch. 2.5 - Find the inverse, if it exists, for each matrix. [...Ch. 2.5 - Prob. 24E Ch. 2.5 - Prob. 25E Ch. 2.5 - Prob. 26E Ch. 2.5 - Prob. 27E Ch. 2.5 - Solve each system of equations by using the...Ch. 2.5 - Solve each system of equations by using the...Ch. 2.5 - Prob. 30E Ch. 2.5 - Prob. 31E Ch. 2.5 - Prob. 32E Ch. 2.5 - Prob. 33E Ch. 2.5 - Solve each system of equations by using the...Ch. 2.5 - Solve each system of equations by using the...Ch. 2.5 - Prob. 36E Ch. 2.5 - Prob. 37E Ch. 2.5 - Prob. 38E Ch. 2.5 - Prob. 39E Ch. 2.5 - Prob. 40E Ch. 2.5 - Prob. 41E Ch. 2.5 - Prob. 42E Ch. 2.5 - Prob. 43E Ch. 2.5 - Prob. 44E Ch. 2.5 - Prob. 45E Ch. 2.5 - Prob. 46E Ch. 2.5 - Prob. 47E Ch. 2.5 - Prob. 48E Ch. 2.5 - Prob. 49E Ch. 2.5 - Prob. 50E Ch. 2.5 - Prob. 51E Ch. 2.5 - Prob. 52E Ch. 2.5 - Prob. 53E Ch. 2.5 - Prob. 54E Ch. 2.5 - Prob. 55E Ch. 2.5 - Prob. 56E Ch. 2.5 - Prob. 57E Ch. 2.5 - Prob. 58E Ch. 2.5 - Prob. 59E Ch. 2.5 - Prob. 60E Ch. 2.5 - Prob. 61E Ch. 2.5 - Solve each exercise by using the inverse of the...Ch. 2.5 - Prob. 63E Ch. 2.5 - Solve each exercise by using the inverse of the...Ch. 2.5 - Prob. 65E Ch. 2.5 - Solve each exercise by using the inverse of the...Ch. 2.6 - Find the production matrix for the following...Ch. 2.6 - Prob. 2E Ch. 2.6 - Prob. 3E Ch. 2.6 - Prob. 4E Ch. 2.6 - Prob. 5E Ch. 2.6 - Prob. 6E Ch. 2.6 - Prob. 7E Ch. 2.6 - Find the ratios of products A, B, and C using a...Ch. 2.6 - Prob. 9E Ch. 2.6 - Use a graphing calculator or computer to find the...Ch. 2.6 - Prob. 11E Ch. 2.6 - Input-Output Open Model In Exercises 11 and 12,...Ch. 2.6 - Prob. 13E Ch. 2.6 - Prob. 14E Ch. 2.6 - Input-Output Open Model In Exercises 13-16, refer...Ch. 2.6 - Input-Output Open Model In Exercises 13- refer to...Ch. 2.6 - Input-Output Open Model A primitive economy...Ch. 2.6 - Prob. 18E Ch. 2.6 - Prob. 19E Ch. 2.6 - Prob. 20E Ch. 2.6 - 21. Israeli Economy An analysis of the 1958...Ch. 2.6 - 22. Chinese Economy The 1981 Chinese economy can...Ch. 2.6 - Prob. 23E Ch. 2.6 - Prob. 24E Ch. 2.6 - Prob. 25E Ch. 2.6 - Prob. 26E Ch. 2.6 - 27. Input-Output Closed Model Use the...Ch. 2.6 - Input-Output Closed Model Suppose that production...Ch. 2.6 - Prob. 29E Ch. 2 - Find the second-order contact matrix PQ mentioned...Ch. 2 - Prob. 2EA Ch. 2 - Prob. 3EA Ch. 2 - Prob. 4EA Ch. 2 - Prob. 5EA Ch. 2 - Prob. 1RE Ch. 2 - Determine whether each of the following statements...Ch. 2 - Prob. 3RE Ch. 2 - Prob. 4RE Ch. 2 - Prob. 5RE Ch. 2 - Prob. 6RE Ch. 2 - Prob. 7RE Ch. 2 - Prob. 8RE Ch. 2 - Prob. 9RE Ch. 2 - Prob. 10RE Ch. 2 - Prob. 11RE Ch. 2 - Prob. 12RE Ch. 2 - Prob. 13RE Ch. 2 - Prob. 14RE Ch. 2 - Prob. 15RE Ch. 2 - Prob. 16RE Ch. 2 - Prob. 17RE Ch. 2 - Prob. 18RE Ch. 2 - Solve each system by the echelon method. 19. 2x -...Ch. 2 - Prob. 20RE Ch. 2 - Solve each system by the echelon method. 2x - 3y +...Ch. 2 - Prob. 22RE Ch. 2 - Prob. 23RE Ch. 2 - Prob. 24RE Ch. 2 - Prob. 25RE Ch. 2 - Prob. 26RE Ch. 2 - Prob. 27RE Ch. 2 - Prob. 28RE Ch. 2 - Prob. 29RE Ch. 2 - Prob. 30RE Ch. 2 - Prob. 31RE Ch. 2 - Prob. 32RE Ch. 2 - Prob. 33RE Ch. 2 - Prob. 34RE Ch. 2 - Prob. 35RE Ch. 2 - Prob. 36RE Ch. 2 - Prob. 37RE Ch. 2 - Prob. 38RE Ch. 2 - Prob. 39RE Ch. 2 - Given the matrices A=[ 4102369],B=[ 232240012],C=[...Ch. 2 - Prob. 41RE Ch. 2 - Prob. 42RE Ch. 2 - Prob. 43RE Ch. 2 - Prob. 44RE Ch. 2 - Prob. 45RE Ch. 2 - Prob. 46RE Ch. 2 - Prob. 47RE Ch. 2 - Prob. 48RE Ch. 2 - Prob. 49RE Ch. 2 - Prob. 50RE Ch. 2 - Prob. 51RE Ch. 2 - Find the inverse of each matrix that has an...Ch. 2 - Prob. 53RE Ch. 2 - Prob. 54RE Ch. 2 - Prob. 55RE Ch. 2 - Prob. 56RE Ch. 2 - Prob. 57RE Ch. 2 - Prob. 58RE Ch. 2 - Prob. 59RE Ch. 2 - Prob. 60RE Ch. 2 - Prob. 61RE Ch. 2 - Prob. 62RE Ch. 2 - Prob. 63RE Ch. 2 - Prob. 64RE Ch. 2 - Prob. 65RE Ch. 2 - Prob. 66RE Ch. 2 - Prob. 67RE Ch. 2 - Prob. 68RE Ch. 2 - Prob. 69RE Ch. 2 - Prob. 70RE Ch. 2 - Prob. 71RE Ch. 2 - Filling Orders A printer has three orders for...Ch. 2 - 73. Input-Output An economy depends on two...Ch. 2 - 74. Nebraska The 1970 economy of the state of...Ch. 2 - Prob. 75RE Ch. 2 - Prob. 76RE Ch. 2 - Prob. 77RE Ch. 2 - Prob. 78RE Ch. 2 - Prob. 79RE Ch. 2 - Prob. 80RE Ch. 2 - Prob. 81RE Ch. 2 - Prob. 82RE Ch. 2 - Prob. 83RE Ch. 2 - 84. Baseball In the 2009 Major League Baseball...Ch. 2 - Prob. 85RE

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Solution Summary: The author explains how to determine the total number of female owls for each of the next five years.

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Chapter 2 Solutions