Explanation Given Information: The matrix showing population of spotted owl in initial year is, X 0 = [ 650 200 2100 ] Matrix A is provided as, A = [ 0 0 0.33 0.18 0 0 0 0.71 0.94 ] Calculation: From exercise 6, the general formula for calculating population change can be written as: B n = [ A ] n * B , where, the matrix [ X 0 ] = [ B ] . Consider that X 0 = [ 650 200 2100 ] and A = [ 0 0 0.33 0.18 0 0 0 0.71 0.94 ] . Let the matrix [ X 0 ] = [ B ] . So, B = [ 650 200 2100 ] Using the general formula for calculating population as B n = [ A ] n * B , calculate the total population for first five years and projection population matrix after 50 years, after 100 years and after 150 years by graphing calculator. Now, compute the product [ A ] n * B of the matrices A and B using the TI- 83 graphing calculator as follows: Step 1. Press “MODE” key and then set “Float” to 0 . Step 2. Press “2nd” key and then press “ x − 1 ” key, a window will appear consisting of three options. Step 3. Now, go to the “EDIT” option and press “ENTER” key. Step 4. Insert the order of the matrix for matrix A , which is 3 × 3 followed by inserting the entries of the matrix. Press “ENTER” key every time an entry is inserted. Step 5. Now, press “2nd” key followed by pressing “MODE” key to clear the window. Step 6. Again, press “2nd” key and then press “ x − 1 ” key, go to “EDIT” option then press the down arrow key and press “ENTER”. Step 7. Insert the order of the matrix for matrix B , which is 3 × 1 followed by inserting the entries of the matrix. Press “ENTER” key every time an entry is inserted. Step 8. Now, press “2nd” key followed by pressing “MODE” key to clear the window. Step 9. Press “2nd” key and then press “ x − 1 ” key, matrix [ A ] will appear. Press “ENTER” key and insert the ^ sign and value of n as 1 and insert the × sign. Step 10. Now, press “2nd” key followed by pressing “MODE” key to clear the window. Again, press “2nd” key and then go to the option 2 : [ B ] and then press “ENTER” twice. Step 11. Repeat step 9 and step 10 by putting different values of to obtain further matrices

Finite Mathematics & Its Applications (12th Edition)

12th Edition

ISBN: 9780134437767

Author: Larry J. Goldstein, David I. Schneider, Martha J. Siegel, Steven Hair

Publisher: PEARSON

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Chapter 2, Problem 8P

To determine

To calculate: The total population for the first five years when the number .18 is increased to .26 and repeat the exercise 7 to determine whether the extinction could be avoided if the matrix showing population of spotted owl in initial year is, X0=[6502002100] and the matrix showing change in population is provided as, A=[000.330.180000.710.94].

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Chapter 2, Problem 7P

Chapter 3.1, Problem 1CYU

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Chapter 2 Solutions

Finite Mathematics & Its Applications (12th Edition)

Ch. 2.1 - 1. Determine whether the following systems of...Ch. 2.1 - Give the meaning of each of the following...Ch. 2.1 - 3. Perform the indicated elementary row...Ch. 2.1 - State the next elementary row operation that...Ch. 2.1 - In Exercises 1–8, perform the indicated elementary...Ch. 2.1 - Prob. 2E Ch. 2.1 - In Exercises 1–8, perform the indicated elementary...Ch. 2.1 - In Exercises 1–8, perform the indicated elementary...Ch. 2.1 - In Exercises 18, perform the indicated elementary...Ch. 2.1 - In Exercises 18, perform the indicated elementary...

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Solution Summary: The author calculates the total population for the first five years when the number .18 is increased to .26 and repeat the exercise 7 to determine whether the extinction could be avoided.

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