3. Uoft bookstore sells books. At the bookstore, UofT displays the number of books that are in store. Every time a book enters the store, a worker will update the display of the current number of books. This update costs UofT a + bk dollars for k digit changes, where a, b are positive real numbers. For example, if a book enters as the 2000-th book, then the cost of changing the display is a + 4b (1999 to 2000 differs in 4 digits). Denote Insert() as the event of a new book coming to UofT bookstore. Using the potential method, prove that the amortized cost for the Insert() is a + dollars. We assume books cannot be removed from the store, and imagine that there are infinite zeroes at the left of the number, so 999 to 1000 changes 4 digits. 106 9 (Hint: The more nines in the end, the more expensive the update cost)