1. [5 marks] Let 0,532 f c is continuous.14' The differential equation (d) [4 marks] Draw the slope eld for the differential equation on the axes below. On Q 2 r P 1 _ E _ h R the slope eld, draw at least four solutions, dt K where r > h and K are positive constants, describes the growth rate of a population P P over time t (a) [4 marks] Find the steady states and indicate them clearly on the phase line below, along with arrows indicating the sign of % between steady states, (e) [2 marks] The term hP in the differential equation represents variable harvest, in which the population is \"harvested\" at a rate proportional to the present popula- P tion. In a few sentences, describe carefully what the model predicts will happen to populations if the parameter h is larger than 1". (b) [1 mark] Given an initial population P(0) = 1,5K, does the model predict that the population will increase or decrease? Answer: (c) [1 mark] Given a very small positive initial population 19(0), what will the popu lation be at the moment it is changing most rapidly? Your answer may include the terms 7*, h and K. (f) [2 marks] Suppose h : 0. In a few sentences, speculate what X represents in terms of population