Question

need answer for qustion2&3.

5:17 childsmath.ca on the answer sheet below. Problem #1: On a certain island, there is a population of snakes foxes, hawks and mice. Their populations at time t are given by st), f(), h), and m(t) respectively The populations grow at rates given by the differential equations 0h + h'= m - 4+- m' u유-49 +/준-s유 Putting the y) [s)f() h() m(t)]7, this system can be written as y' Ay four populations into vector Find the eigenvectors and eigenvalues of A. Label the eigenvectors x through X4 in order from largest eigenvalue to smallest (the smallest being negative). Scale each eigenvector so that its first component is 1 When you have done so, identify the eigenvector whose fourth component is the largest. What is that largest fourth component? Problem #1: 14 Just Save Submit Problem #1 for Grading Attempt #2 Attempt #3 Problem #1 Attempt #1 Your Answer: 14 Your Mark: 3/3 5:17 childsmath.ca Problem #2: Continuing from the system of differential equations from Problem 1, each eigenvector represents grouping of animals that changes with simple exponential growth or decay. The exponential rate of growth eigenvalue. Because the matrix A is invertible and diagonalizable, any initial values for the animal population can be written as a combination of these four special groupings that each grow exponentially by their eigenvalue a decay is given by the corresponding or Consider the initial population y(0)[24 20 12 141]7. Solve for constants c through c4 in order to write y(0) c X c2x2 + c3x3 + C4X4 where x through x4 are the eigenvectors as detailed in Problem (i.e., the eigenvectors in order, and scaled so that the first component is 1) Enter the values of c, c2, c3, and c4, separated with commas Problem #2: 4,7,5,8 Submit Problem # 2 for Grading Just Save Attempt #2 Attempt #1 Attempt #3 Problem #2 Your Answer: 4,7,5,8 Your Mark: 1/4x Note: Your mark on each question will be the MAXIMUM of your marks on each try. (So there is no harm in making another attempt at a partially correct answer.) 5:17 childsmath.ca scaled so that the first component is 1) Enter the values of ci, c2, c3, and c4 separated with commas 4,7,5,8 Problem #2: Just Save Submit Problem # 2 for Grading Attempt #2 Attempt #3 Attempt #1 Problem #2 Your Answer: 4,7,5,8 1/4 x Your Mark: Note: Your mark on each question will be the MAXIMUM of your marks on each try (So there is no harm in making another attempt at a partially correct answer.) Problem #3: Based on the system of differential equations from Problem 1, with the initial population from problem 2, find the function for the population of mice, m(t) Enter your answer as a symbolic function of t, as in Problem #3: these examples Submit Problem # 3 for Grading Just Save Attempt #1 Attempt #2 Attempt #3 Problem #3 Your Answer: Your Mark:

Answer 1

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