Step 1 :Recognize the pattern in the sequence: $100,105,110.25, \ldots$
Step 2 :Observe that the amount of money in the account increases by 5% each year. This is because the difference between 105 and 100 is 5, which is 5% of 100. Similarly, the difference between 110.25 and 105 is 5.25, which is 5% of 105.
Step 3 :Therefore, the recursive formula that can be used to determine the total amount of money earned in any year based on the amount earned in the previous year is $f(n+1)=1.05 f(n)$
Step 4 :The final answer is: \(\boxed{f(n+1)=1.05 f(n)}\)