Question

The sequence below represents Marisa’s fine at the library for each day that she has an overdue book:

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

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

We see the fine increases by $0.15 each day, so it's an arithmetic sequence with difference $0.15 and first term $0.50 (when n = 1).

Let f(n) = 0.15n + b. Using f(1) = 0.50 gives 0.15(1) + b = 0.50 → b = 0.35.

Thus f(n) = 0.15n + 0.35.