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### حل تمارين الفصل الثاني ( نمذجة ومحاكاة ) - Exercise Questions and Case Study Chapter 2 -Solution

Chapter 2

1). If three customers arrived to a supermarket in the morning at 9:00, 10:00 and 11:00 am respectively, they took 10, 20 and 30 minutes in separate counters. Calculate C1, C2, C3.

2). Calculate the Average Interarriaval time of t1 (12:10), t2(12:30), t3 (12:50), and t4(12:58).

3). Apply Predator-Prey simulation Model for calculating the “Rate of change of the prey population”

if r=10, X(t)=200, a=10 and y(t)=180.

4). Use the Predator-Prey simulation Model for finding the Rate of change of the Predator population with s=5, X(t)=200, b=5 and y(t)=180.

Case Study: Investigating a Predator-Prey Relationship

In this case study you will investigate one of the most famous sets of data ever collected on a predator-prey relationship.

Lynx, a cat of forests of Canada, prey on snowshoe hare. In some areas, hare provide over 70 % of the lynx diet. As a result, the population growth curve of the lynx should show a relationship to that of the hare. What do you think that relationship is?

The data on this relationship are listed in the following table. Study them carefully as you answer the questions.

 Population Numbers Of Hare and Lynx by Year Year Hare numbers Lynx numbers Year Hare numbers Lynx numbers 1895 1900 1903 1905 1908 1909 1910 1912 1915 85 000 18 000 65 000 40 000 28 000 25 000 51 000 70 000 30 000 48 000 6 000 18 000 61 000 28 000 4 000 10 000 32 000 42 000 1918 1921 1924 1927 1930 1933 1934 1936 5 000 52 000 78 000 18 000 4 000 22 000 86 000 15 000 5 000 11 000 28 000 42 000 5 000 18 000 32 000 40 000

Questions
5. Plot this data on the same sheet of graph paper. Put the year on the x-axis and the population numbers on the y-axis.
6. Which animal is the predator and which is the prey?
7. As the hare population increases what happens to the lynx population? Why?
8. As the lynx population increases what happens to the hare population? Why?
9. a) These population growth curves are said to fluctuate. What does that mean?
b) How many years are there in one fluctuating cycle of the hare population?
10. What factors may be responsible for the unusual number of hare in 1895?
11. We say that a good predator-prey relationship keeps the two populations “in balance.” What is meant by this?
12. What would happen to the forest environment if the lynx started being hunted for their skins?

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