Reconsider the tree problem like we did in class (in Ex. 3.12 and Ex. 3.13). Now assume that the hardwoods grow at a rate of 5% per year, while the softwoods grow at a rate of 15% per year. Assume that in a certain forest, the carrying capacity for hardwoods is 5,000 tons per acre, and for softwoods it is 10,000 tons per acre. Assume also that the competition factor has become too great to allow the coexistence of both species of trees (suppose = 0.8 for = 1,2). (a) Sketch and label the vector field for the model. Indicate the location of each equilibrium in the state space. (b) For each equilibrium point, determine the linear system that approximates the behaviour of the original dynamical system in the neighbourhood of the equilibrium. Write the general solution to the linear system and sketch the linear phase portrait. (c) Sketch the complete phase portrait for the nonlinear model using your sketches from (a) and (b). (d) What does the model predict about the future of this forest