ws20 - Math 464, Worksheet 20 Use your model from Worksheet...

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Unformatted text preview: Math 464, Worksheet 20 Use your model from Worksheet 19: R − 0.002RF 100 ∆F = 0.0004RF − 0.01F ∆R = 0.02R 1 − 1. Use Excel to generate a solution for this model with initial conditions R(0) = 2 and F (0) = 10. 2. Graph the solution functions R(t) and F (t). 3. Extend your solution until you have at least three local maxima in each function. 4. Graph the solution as a parametric plot in R-F axes. 5. How long does it take for the solution to make one “cycle”? More specifically: (a) Compute the time between local maxima on the R(t) graph. Repeat until you run out of visible maxima. (b) Repeat for the local minima on R(t). (c) Repeat for maxima/minima on the F (t) graph. 6. Repeat Problems 1-4 for each of the following initial conditions. If the solutions oscillate, also repeat Problem 5. (a) R(0) = 50 and F (0) = 0 (b) R(0) = 0 and F (0) = 50 (c) R(0) = 50 and F (0) = 50 (d) R(0) = 150 and F (0) = 0 (e) R(0) = 150 and F (0) = 50 7. Try to find some initial values F (0) and R(0), both non-zero, so that the solutions do not oscillate. 8. Try to find some initial values so that the solution oscillates with a “period” distinctly different from earlier problems. 1 ...
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