$(25$ pts$)$

$($a$)$ How many keys $($records$)$ and how many nodes does the following B tree contain?

$($b$)$ Proof:

If $n1,$ the number of keys currently stored in the $B$ tree, $t$ is the minimum degree

of the $B-$Tree, and $h$ is the worst case height of the $B$ tree,

prove that $hlog[\frac{n+1}{2}]$ with base $t.$

$1$ node,

$1000$ keys