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a 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 = 0.03y (1-1) (-1) dt 100 a) Find the equilibrium points of the DE (-). b) Construct the sign chart of f(u) = 0.03 y (1 - i)(-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 that can be sustained over an indefinitely long period of time? (L is called the carrying capacity of the environment and the sparsity constant).