Question

The sequence below shows Marisa’s library fine starting on the first day her book is overdue and for each additional day afterward:

$0.50, $0.65, $0.80, $0.95, $1.10, ...

Let f(n) represent Marisa’s library fine (in dollars), where n is the number of days the book has been overdue, starting with n=1 for the first day overdue.

Which equation represents Marisa’s library fine as a function of a book that is n days overdue?

f(n) = 0.15n
f(n) = 0.50n
f(n) = 0.15n + 0.35
f(n) = 0.50n + 0.15

Answer 1

The sequence is arithmetic with first term 0.50 and common difference 0.15. So
f(n) = 0.50 + (n−1)(0.15) = 0.15n + 0.35.
Thus f(n) = 0.15n + 0.35.