(2) Equipped with the experience you gained with the previous prob- lem, let us analyze the [to-called logistic growth population model: %=I(P)=rP(I). (2) where r and M are positive constants. Your TA will explain how this model is the simplest one that accounts for nite resources. (a) Draw the polynomial HP). Be sure to nd and label its roots. Roots: (b) Draw arrows on indicating where P is increasing/decreasing. (c) What is the behavior of the logistic model in the long run (t i +00) ifone starts with an initial P(t =0) = P0 such that: (l) Pu ispreciaely at oneofthe roots: (ii) P;I is just to the right of the rst root: (iii) P0 is to the right of the last root: (ti) (i) What happens to initial conditions very close to each one the xed points? Do they get \"attracted\" or epelled\" away from them? (ii) Why is M called the carrying capacity? (iii) Why is logistic growth equivalent to exponential (3.1.1.3. Malthnnian) growth [de/dt = k PM] for small populations? Small with respect to what