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The evolution of a population of Hippos, R(t), in hundreds, time in years, in an African National Park is given by the equation, dR dt (a) Solve the system exactly for R(t). = R(7 – R); R(0) = 3 2 (b) What happens as the time t → ∞o, i.e. what is the population a long time in the future? (c) Write an Euler scheme and compute until the population levels off (using Excel, Matlab, Octave, LibreCalc or similar). Do it twice, once with At = 0.1 and once with At = 0.05. (d) Plot all of your solutions on the same set of axes and comment.

The evolution of a population of Hippos, R(t), in hundreds, time in years, in an African National Park is given by the equation, dR dt (a) Solve the system exactly for R(t). = R(7 – R); R(0) = 3 2 (b) What happens as the time t → ∞o, i.e. what is the population a long time in the future? (c) Write an Euler scheme and compute until the population levels off (using Excel, Matlab, Octave, LibreCalc or similar). Do it twice, once with At = 0.1 and once with At = 0.05. (d) Plot all of your solutions on the same set of axes and comment.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section: Chapter Questions
Problem 4RE
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The evolution of a population of Hippos, R(t), in hundreds, time in years, in an African National Park is given by the equation, dR dt (a) Solve the system exactly for R(t). = R(7 – R); R(0) = 3 2 (b) What happens as the time t → ∞o, i.e. what is the population a long time in the future? (c) Write an Euler scheme and compute until the population levels off (using Excel, Matlab, Octave, LibreCalc or similar). Do it twice, once with At = 0.1 and once with At = 0.05. (d) Plot all of your solutions on the same set of axes and comment.
Transcribed Image Text:The evolution of a population of Hippos, R(t), in hundreds, time in years, in an African National Park is given by the equation, dR dt (a) Solve the system exactly for R(t). = R(7 – R); R(0) = 3 2 (b) What happens as the time t → ∞o, i.e. what is the population a long time in the future? (c) Write an Euler scheme and compute until the population levels off (using Excel, Matlab, Octave, LibreCalc or similar). Do it twice, once with At = 0.1 and once with At = 0.05. (d) Plot all of your solutions on the same set of axes and comment.
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