Answer Happy

B.2 An enthusiastic physics student constructed a model to describe the size of the bee population in Britain. If B(t) describes the number of bees as a function of time, she found that B(t) satisfies dB 2 - 3t+2 B=0, dt + P t+1 where p is a constant quantifying the effect of pesticides. [8] [6] (a) Find B(t) in terms of t, p and Bo, where B, is a positive constant and B = B. when t = 0. (b) Show that B(t) has two stationary values whose ratio is (3/2)*pe-5p/2. (c) Describe the behaviour of B(t) as t + too for the case where p > 0 and for the case where p <0. In separate diagrams, sketch the graph of y = B(t) fort > 0 for each of these cases. [2] [4]