$(5$ points$)$ Consider the recursion u$\_($t$)=3$u$\_($t$-1)-$b $.($a$)$ Find the value of b such that the equilibrium solution of this recursion is hat$($u$)=500.($b$)$ Using the value of b you found in question $($a$),$ make a change of variables and show how this change transforms the affine geometric recursion u$\_($t$)=3$u$\_($t$-1)-$b to a geometric recursion of the form v$\_($t$)=\backslash$lambda v$\_($t$-1).$