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

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 Exercise Questions and Case Study

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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