Final answer:
The amount of money owed to the library is dependent on the number of days a book is overdue, a mathematical relationship where a fixed base fee is combined with a daily fee multiplied by the number of overdue days.
Step-by-step explanation:
The question at hand requires an understanding of how one variable affects another, a key concept in mathematics. In this scenario, the amount of money you owe the library is directly dependent on the number of days your book is overdue. If we reference the given information that a credit card company charges $10 when a payment is late and $5 a day thereafter, we can draw a parallel to a library fine system where there's typically a base fee for late returns, followed by a daily accruing fee.
To demonstrate this mathematically, if a book is overdue for x days, the total fine (F) could be represented as F = (Base fee) + (Daily fee) * x. Substituting the credit card company's fees into this equation as an example, F = $10 + $5 * x. This formula illustrates that the total amount you owe increases with each additional day the book remains unreturned, showcasing the dependency of the total fine on the number of days late.