The initial value refers to the fine owed when the book is not overdue, which means it is when the number of overdue days is zero. Based on the provided table, it implies that the fines start accumulating after the book is overdue for at least 2 days, with a fine of 30 cents.
Since no fines are listed for 0 days overdue, we can infer that the initial fine for a book that is not overdue (0 days) is 0 cents.
So, the initial value is:
0 cents.