Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
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Problem I. 114. (October 2005)

I. 114. There are foxes and rabbits living on an island. The reproductive rabbit population increases by m percent in each month. However, foxes prey on the rabbits: one fox eats p percent of the total rabbit population in each month -- provided that there are enough rabbits. The fox population increases proportionally to the available food: in every month each rabbit accounts for n percent of them giving birth to a baby fox, but q percent of the total fox population dies.

Make an Excel sheet into which the values of n, m, p, q and the population sizes in the first month can be entered, then it computes the population sizes in the following 60 months. If meanwhile any (or both) species became extinct, the program should mark the name of that species red. You should also make two plots, the first one representing the sizes of the two populations as a function of time, while the second one graphing the ratio of the populations.

The sheet (i114.xls) should be submitted.

(10 pont)

Deadline expired on November 15, 2005.

Solution (in Hungarian)


32 students sent a solution.
10 points:Balambér Dávid, Czigler András, Gilián Zoltán, Gombkötő Tamás, Györök Péter, Hunyady Márton, Kiss Dániel Miklós, Kovács 129 Péter, Kuslics Ferenc, Ozsvárt László, Pétercsák Richárd, Szakács Nóra, Szoldatics András, Vecsey Dénes.
9 points:Biró 123 János.
8 points:5 students.
6 points:6 students.
5 points:4 students.
4 points:1 student.
Unfair, not evaluated:1 solution.

Problems in Information Technology of KöMaL, October 2005