1. Two species are said to be symbiotes if they help each other to survive. For instance, clown fish and sea anemones are symbiotes (they protect each other from different types of predators). Say in some region, without sea anemones to shelter them, the clown fish population is stable (that is, the clown fish population in the k + 1-th season is the same as the population in the k-th season). However, for each sea anemone present, an extra 0.2 clown fish are present in the next season. Similarly, in the absence of clown fish, the sea anemone population in the k + 1-th season is only 70% of the population in the k-th season. However, for each clown fish present, an extra 0.2 anemones are present the next season. (a) Write down difference equations for the number of clown fish and sea anemones in the k + 1-th season in terms of the clown fish ck and sea anemones az in the k-th season. (b) Write the system of difference equations above as a matrix equation, then diago- nalize the matrix.

1. Two species are said to be symbiotes if they help each other to survive. For instance, clown fish and sea anemones are symbiotes (they protect each other from different types of predators). Say in some region, without sea anemones to shelter them, the clown fish population is stable (that is, the clown fish population in the k + 1-th season is the same as the population in the k-th season). However, for each sea anemone present, an extra 0.2 clown fish are present in the next season. Similarly, in the absence of clown fish, the sea anemone population in the k + 1-th season is only 70% of the population in the k-th season. However, for each clown fish present, an extra 0.2 anemones are present the next season. (a) Write down difference equations for the number of clown fish and sea anemones in the k + 1-th season in terms of the clown fish ck and sea anemones az in the k-th season. (b) Write the system of difference equations above as a matrix equation, then diago- nalize the matrix.

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Question

1. Two species are said to be symbiotes if they help each other to survive. For instance,
elown fish and sea anemones are symbiotes (they protect each other from different
types of predators).
Say in some region, without sea anemones to shelter them, the clown fish population
is stable (that is, the clown fish population in the k + 1-th season is the same as the
population in the k-th season). However, for each sea anemone present, an extra 0.2
clown fish are present in the next season.
Similarly, in the absence of clown fish, the sea anemone population in the k + 1-th
season is only 70% of the population in the k-th season. However, for each clown fish
present, an extra 0.2 anemones are present the next season.
(a) Write down difference equations for the number of clown fish and sea anemones
in the k + 1-th season in terms of the clown fish c& and sea anemones ar in the
k-th season.
(b) Write the system of difference equations above as a matrix equation, then diago-
nalize the matrix.

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