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7. A model by J.R. Hicks uses the following difference equation: Yi+2 - (b+k) Yt+1+kY, = a (1+g), t=0,1,... where a,b,g, k are positive constants. (a) Find a particular solution Y of the equation assuming that (1+g)-(6+k:)(1+9)+k+ 0. (b) Give conditions for the characteristic equation to have two complex roots. (e) Find the growth factor r of the oscillations when the conditions obtained in part (6) are satisfied, and determine when the oscillations are damped