The plant model we covered in class is Pn+1 = apn+bpn-1 where a, b > 0. As you know, the solution is given by Pn = C+CA2 where A = a + b. (a) Find a threshold ac such that the plants go extinct (pn 0 as n ) when 0 < a < ac, and plants grow exponentially, (pn as n ) when a > ac. Note that ac will depend on b. (b) Suppose that a = ac (with a, b > 0). What is the long-term behaviour (n ) in this case?