Question

the sequence below represents marisas 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 marisas library fine as a function of a book that is n days overdue? \bigcirc f(n) = 0.15n \bigcirc f(n) = 0.50n \bigcirc f(n) = 0.15n + 0.35 \bigcirc f(n) = 0.50n + 0.15

Explanation:

Step1: Identify Sequence Type

The sequence is arithmetic (common difference $d = 0.65 - 0.50 = 0.15$). Arithmetic sequence formula: $f(n)=f(1)+(n - 1)d$. Here, $f(1)=0.50$, $d = 0.15$.

Step2: Derive the Formula

Substitute into formula: $f(n)=0.50+(n - 1)(0.15)$. Simplify: $f(n)=0.50 + 0.15n-0.15=0.15n + 0.35$.

Step3: Verify with n=1

For $n = 1$, $f(1)=0.15(1)+0.35 = 0.50$, matches. For $n = 2$, $0.15(2)+0.35 = 0.65$, matches.

Answer:

$f(n)=0.15n + 0.35$ (the third option: $f(n)=0.15n + 0.35$)