Problem $4[24$ pts$]$: Recurrence Solve the following recurrences by substitution. Assume a base case of T $(1)=1.$ As part of your solution, you will need to establish a pattern for what the recurrence looks like after the k$-$th substitution. Check that this pattern is consistent with your substitutions, but you do not need to formally prove it is correct via induction.

i$)$ T $($n$)=$ T $($n $2)7$