Each system of differential equations is a model for two species that either compete for the same resources or cooperate for mutual benefit (flowering plants and insect pollinators, for instance). Decide which of the following systems describes the competition model. 50% 1. 50% 2. 1 2 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 33% 1. 33% 33% At t = 3 the population of species 1 reaches a maximum of about 200. At t = 2 the population of species 2 reaches a maximum of about 100. At t = 2 the population of species 2 reaches a maximum of about 190 2. 3. 1 2 3 4 5 6 7 8 9 10 11 12 13 21 22 23 24 25 26 27 28 29 30 31 32 33 41 42 43 44 45 46 47 48 49 50 1 14 15 16 2 17 18 319 20 34 35 36 37 38 39 40 33% 33% 33% 1. A=9,000,L=400 2. A=10,000,L=400 3. A=8,000,L=200 1 2 3 4 5 6 7 8 9 10 11 12 13 21 22 23 24 25 26 27 28 29 30 31 32 33 41 42 43 44 45 46 47 48 49 50 1 14 15 16 2 17 18 319 20 34 35 36 37 38 39 40 1. Both populations are stable 2. In the absence of wolves, the rabbit population is always 5000 3. Zero populations 33% 1 2 3 4 5 6 7 8 9 10 11 12 13 21 22 23 24 25 26 27 28 29 30 31 32 33 41 42 43 44 45 46 47 48 49 50 1 33% 2 33% 14 15 16 17 18 319 20 34 35 36 37 38 39 40 33% 1. 33% 33% At t = C number of rabbits decreases to about 1000. At t = B the number of foxes reaches a maximum of about 2400. At t = B number of rabbits rebounds to 100. 2. 3. 1 2 3 4 5 6 7 8 9 10 11 12 13 21 22 23 24 25 26 27 28 29 30 31 32 33 41 42 43 44 45 46 47 48 49 50 1 14 15 16 2 17 18 319 20 34 35 36 37 38 39 40
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