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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 RF 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 14 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 nonzero, 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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 Fall '08
 DougBullock
 Math

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