$(10$ pts$)$ Consider the following pseudocode.

function $f(n)$

$1$: $k=o$

$2$: for i from $1ton$

$3$: $j=1$

$4$: while $jn$

$,5$:$k=2^{**}k+1$

$,6$:$j=2^{**}j$

$7$: return $k$

$7$: return $k$

$($a$)$ Calculate the total number of basic operations executed on from Line $2$ to Line $6.$ Justify

your answers. $(5$ pts$)$

Line $1$

$1$

Justification

$1$ assignment $($saving$)$

Tinentn $6$

Line $7$

$2$

Justification$\_1$ return and $1$ loading

$($b$)$ What is the run time of this algorithm in big O notation? Justify your answer.

Total runtime in terms of big $O$ notation $(3pts)$:

Justification $(2$ pts$)$: