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In 2019, A field in California has been completely devastated by fire. Two types of vegetation, grasses and small shrubs, will first begin to grow, but the small shrubs can take over an area only if preceded by the grasses. In the figure below, the transfer coefficient of 0.3 indicates that, by the end of the summer, 30% of the prior bare space in the field becomes occupied by grasses. Bare Space 0.3/year 0.15/year (death) 0.05/year (death) 0.2/year 3 Small Grasses Shrubs (a) Find the transfer matrix T. (11) (b) Suppose X= 0 and the area is measured in acres 0. c) Determine the ground cover in each of the next 4years. (2023?) d) what happens after a long time? Does the system reach any equilibrium? Use eigenvalues and matrix decomposition to justify your answer

In 2019, A field in California has been completely devastated by fire. Two types of vegetation, grasses and small shrubs, will first begin to grow, but the small shrubs can take over an area only if preceded by the grasses. In the figure below, the transfer coefficient of 0.3 indicates that, by the end of the summer, 30% of the prior bare space in the field becomes occupied by grasses. Bare Space 0.3/year 0.15/year (death) 0.05/year (death) 0.2/year 3 Small Grasses Shrubs (a) Find the transfer matrix T. (11) (b) Suppose X= 0 and the area is measured in acres 0. c) Determine the ground cover in each of the next 4years. (2023?) d) what happens after a long time? Does the system reach any equilibrium? Use eigenvalues and matrix decomposition to justify your answer

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.2: Exponential Functions
Problem 53E
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%233 In 2019, A field in California has been completely devastated by fire. Two types of vegetation, grasses and small shrubs, will first begin to grow, but the small shrubs can take over an area only if preceded by the grasses. In the figure below, the transfer coefficient of 0.3 indicates that, by the end of the summer, 30% of the prior bare space in the field becomes occupied by grasses. Bare Space 0.3/year 0.15/year (death) 0.05/year (death) 0.2/year 3 Small Grasses Shrubs (a) Find the transfer matrix T. (b) Suppose X=| 0 | and the area is measured in acres %3D c) Determine the ground cover in each of the next 4years. (2023?) d) what happens after a long time? Does the system reach any equilibrium? Use eigenvalues and matrix decomposition to justify your answer #4 Expand Ax) = 4x² – 1, –1 <x< 1, in a Fourier series and plot in the same graph the function f(xr) and the Fourier approximation up to the fourth term included. Explain The Gibbs Phenomena occurring when approximating. -
Transcribed Image Text:%233 In 2019, A field in California has been completely devastated by fire. Two types of vegetation, grasses and small shrubs, will first begin to grow, but the small shrubs can take over an area only if preceded by the grasses. In the figure below, the transfer coefficient of 0.3 indicates that, by the end of the summer, 30% of the prior bare space in the field becomes occupied by grasses. Bare Space 0.3/year 0.15/year (death) 0.05/year (death) 0.2/year 3 Small Grasses Shrubs (a) Find the transfer matrix T. (b) Suppose X=| 0 | and the area is measured in acres %3D c) Determine the ground cover in each of the next 4years. (2023?) d) what happens after a long time? Does the system reach any equilibrium? Use eigenvalues and matrix decomposition to justify your answer #4 Expand Ax) = 4x² – 1, –1 <x< 1, in a Fourier series and plot in the same graph the function f(xr) and the Fourier approximation up to the fourth term included. Explain The Gibbs Phenomena occurring when approximating. -
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