Given functions T$1$ and T$2$:

$$ Function T$1$:

$$ public int T$1($ int n $)\{$

$$ if $($n $<1)\{$

$$return $0$;

$\}//$ if

else $\{$

$$ return $(2*$n $+$ T$1($ n$-1))$;

$\}//$ else

$\}//$ T$1$

$($a$)$ Set up a recurrence relation for the running time of the function T$1$ as a function of n$.$ Solve your recurrence relation to specify theta bound of T$1.$

Function T$2$:

$$ public int T$2($int n$)\{$

$$ if $($n $<1)\{$

$$ return $0$;

$\}//$ if

$$ else $\{$

$$ return $($T$1($n$)+$ T$2($n$-1)$ n$)$;

$\}//$ else

$\}//$ T$2$

$($b$)$ Now set up a recurrence relation for the running time of the function T$2$ as a function of n$.$ Solve your recurrence relation to specify theta bound of T$2.$