$1.$ Determine the asymptotic complexity of the function defined by the recurrence relation.$$ Justify your solution using a recursion tree.$$ You may not use the Master Theorem as justification of your answer.$$ Simplify and express your answer as $($nk$)$ or $($nk log$2$ n$)$ whenever possible.$$ If the algorithm is exponential just give exponential lower bounds. Assume T$(1)=$ c$.$

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a$)$ T$($n$)=4$T$($n$/4)+$ c

b$)$ T$($n$)=2$T$($n$/2)+$ cn$2$