Overall Time Complexity:

The most significant parts of the code in terms of time complexity are the operations to find the maximum age and the index of the maximum age. Both of these operations have a time complexity of

$$

$($

$$

$)$

O$($n$).$

Conclusion:

The Big Theta $($

$\backslash$Theta

$\backslash$Theta $)$ of the given code is

$\backslash$Theta

$($

$$

$)$

$\backslash$Theta $($n$),$ where

$$

n is the number of elements in the ages list. This is because the code performs two linear scans of the list $($max and index$),$ both of which contribute to the overall time complexity.