ws16 - Math 464, Worksheet 16 Consider two populations of...

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Math 464, Worksheet 16 Consider two populations of animals that compete for space and/or other resources. Either population alone would expand to the limits of its environment, but together each population exerts a negative inFuence on the other. This is represented by b x b y d x d y (-) (-) y x ±or this exercise we will assume: Birth rate of species x is b x = 0 . 02 animals per week. Birth rate of species y is b y = 0 . 03 animals per week. Death rate of species x is d x = 0 . 01 x animals per week. Death rate of species y is d y = 0 . 01 y animals per week. The e²ect of y on x is that each week 0 . 01 xy of species x die o². The e²ect of x on y is that each week 0 . 02 xy of species y die o². 1. Write di²erence equations for the populations x and y . 2. Assume that x (0) = 0. Use qualitative analysis to graph the population y ( t ) on t - y axes for each of: (a) y (0) = 1 (b) y (0) = 3 (c) y (0) = 5 3. ±or each initial population in Problem 2, graph ( x
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ws16 - Math 464, Worksheet 16 Consider two populations of...

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