Consider the difference equation yt+1(a+byt) = cyt, t = 0,1,

Last updated: 8/6/2022

Consider the difference equation yt+1(a+byt) = cyt, t = 0,1, .... , where a, b, and c are positive constants, and yo > 0. Show that yt > 0 for all t. Define xt = 1/yt. Show that by using this substitution the equation turns into the canonical form. Solve the difference equation yt+1(2+3y) = 4yt, assuming that yo =1/2. What is the limit of y, as t → ∞?