Weather is notoriously difficult to predict. Models are subject to chaotic motion and must consider the initial conditions. The famous butterfly effect states that if a butterfly flaps its wings in Tahiti, that small event might cause a hurricane to hit Texas. This leads us to the following model: suppose that weather at time t is always between 0 and 1 and is governed by x_(t+1)=〖4x〗_t (1-x_t ). For x_0 = 0.2 and x_0 = 0.2000001, determine x_1; x_2;… x_50. Assume values for x closer to zero represent mild weather, and closer to 1 represent extreme weather. How do your calculations illustrate the butterfly effect? Support your answer with graphs.

Weather is notoriously difficult to predict. Models are subject to chaotic motion and must consider the initial conditions. The famous butterfly effect states that if a butterfly flaps its wings in Tahiti, that small event might cause a hurricane to hit Texas. This leads us to the following model: suppose that weather at time t is always between 0 and 1 and is governed by x_(t+1)=〖4x〗_t (1-x_t ). For x_0 = 0.2 and x_0 = 0.2000001, determine x_1; x_2;… x_50. Assume values for x closer to zero represent mild weather, and closer to 1 represent extreme weather. How do your calculations illustrate the butterfly effect? Support your answer with graphs.

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter6: Linear Systems

Section6.2: Guassian Elimination And Matrix Methods

Problem 84E: Explain the differences between Gaussian elimination and Gauss-Jordan elimination.

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