Math 464, Worksheet 8
Suppose that a population is divided into Mmature animals and Aadolescents. Assume the
following conditions (as represented in the diagram below):
•Birth rate is b= 0.1 adolescents per day per mature animal.
•Death rate for adolescents is dA= 0.01 per day per adolescent.
•Death rate for mature animals is dM= 0.05 per day per mature animal.
•Adolescents mature into adults at a rate of g= 0.1 per day per adolescent.
dAA
b
gMdM
1. Write difference equations for Aand M.
2. Assuming A(0) = M(0) = 50, compute A(t) for each of the first 500 days.
3. Compute the ratio M(t)/A(t) for each of these days. What is the long term ratio?
4. Graph A(t) and M(t).
5. Repeat Problems 2-4 for A(0) = 40 and M(0) = 60
6. Repeat 2-4 for A(0) = 100 and M(0) = 0
7. Repeat 2-4 for A(0) = 0 and M(0) = 100
8. Repeat Problems 1-6 with an adolescent death rate of dA= 0.1.
9. What happens if dA= 0.5?
10. Experiment with different values of g,band dM.
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