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page 2 No.2 (10 points) The DE (+) below is a Modified Logistic Population model. It describes the population of deer in Texas y y(t) (in thousands of deer) as a function of time t (in years) dy dt y { = 0.03y (1 - 10) (- 1) a) Find the equilibrium points of the DE (*). b) Construct the sign chart of f(y) = 0.03 y (1 - 10) (1 - 1). c) Using part b), determine the intervals (of the y variable) where the solutions y = y(t) of DE (*) are increasing and those where they are decreasing. d) Sketch the phase portrait of the DE (-). Identify each equilibrium point as an attractor (i.e. a sink), a repeller (i.e. a source), or a node. e) Sketch the graph of all solutions of DE (*) on the ty-plane. f) Using your results, what is the largest population L of deer that can be sustained over an indefinitely long period of time? Also, what is smallest (positive) population S that can be sustained over an indefinitely long period of time? (L is called the carrying capacity of the environment and S the sparsity constant).