Before moving on to the discussion, read the discussion of the predator/prey model in the study sheet. Describe an oscillating phenomenon that doesn't converge to a value over time. In mathematical terms, explain a quantityg(t)such thatg(t)doesn't exist because the function oscillates.

Statistics Discussion Page 1 of The Predator] Prey Model In a predatorfprey relationship, such as between foxes and rabbits, the population growth of one species depends on the number of animals in the other. The more foxes there are, the more rabbits will be eaten, and the number of rabbits will go down. [in the other hand if there aren't enough rabbits to eat, the number of foxes will decrease. This type of interaction is very complex. We'll use a simplified version of it here. If we start with a lot of rabbits and not many foxes, the following cycle will occur: 1. Lots of Iabbits, not many foxes. Results in: increase in fox population (leis of mbbits to eat}, which in turn leads to: 2. Lots of Iabbits, lots of foxes. Results in: decrease in rabbit population {lots of Iabbits being eaten], which in turn leads to: 3. Not many rabbits, lots of foxes. Results in: decrease in fox population {lots of starving foxes), which in turn leads to: 4. Not many rabbits, not many foxes. Results in: increase in rabbit population {not many foxes to eat rabbits}, which in turn leads to: 5. Lots of Iabbits, not many foxes... And the cycle goes on and on. We can graph this as follows: where the blue curve is the number of rabbits (in hundreds), and the red curve is the number of foxes (actual numbers}. . 11m r) Notice that if x} is the number of foxes, then 1"\": =DNE because of its oscillating nature. The exact solution of problems such as these requires differential equations