Index of Element in Array $($Permutation$)$

The following algorithm finds the index of an element in an array of integers, or None if it is not found. def find$\_$element$\_$index$($a$,$ x$)$:

# Get length of array

n $=$ len$($a$)$

# Iterate over all elements

for i in range$($n$)$:

# Get value of element

val $=$ a$[$i$]$

# Check element found

if val $==$ x:

# Return current index as found

return i

# Return not found

return None

If the array is a permutation of the numbers from $0$ to n $-1,$ and the element to find is within that range, the following is requested:

$($a$)$ Find the expression for the expected value of the growth order in terms of the size n of the array.

$($b$)$ The expression of the growth order according to the asymptotic notation O$().$

$($c$)$ How would you reconcile the two previous answers?