Question $13$: Amortized Analysis Example $(5$ points$)$

Task: Simulate a dynamic array in Python that resizes itself when it reaches capacity $($doubling its size$).$ Implement a function to perform a sequence of insertions and print the array's capacity after each insertion. Analyze the amortized cost of insertions and explain how the amortized analysis ensures that the average insertion time is $O(1).(5$ points$)$