Could someone please check my work

Consider the following dynamical system. an+1 = 0.7an + 0.1, do = 0.5 a Find a equilibrium value and classify the equlibrium value. b) Find the solution an. ) r= 0.7 b= 0.1 anti = ra , + 6 37 an = rect For a = 0 . 7 a + 0. 1 a= b 7 0.3a = 0. 1 OR 7 a= /3) 0 . 1 - 0 .7 The equilibrium value, a, is stable Since |r/21 . equilibrium b ) Find a= [' Value /3 + Fr using initial condition, a. = 0.5 : Q . = 0.5 = 0.7 c + 1/ 3 2 0.5 = C + /3 7 C = - Solution Hence, a = 0. 7 ( 5 ) + 3