Solving recurrences using the Substitution method. Give asymptotic upper and lower

bounds for T$($n$)$ in each of the following recurrences. Solve using the substitution

method. Assume that T$($n$)$ is constant n $<=2.$ Make your bounds as tight as possible and

justify your answers. Hint: You may use the recursion trees or Master method to make

an initial guess and prove it through induction.

a$.$T$($n$)=2$T$($n$-1)+1$

b$.$T$($n$)=8$T$($n$/2)+$ n$^3$