the sequence below represents marisas fine at the library for each day that she has an overdue book: $0.50…

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

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

Answer

Explanation:

Step1: Identify the type of sequence

The sequence $0.50, 0.65, 0.80, 0.95, 1.10,\cdots$ is an arithmetic - sequence. The common difference $d$ between consecutive terms can be found by subtracting the first term from the second term. $d=0.65 - 0.50=0.15$.

Step2: Recall the formula for an arithmetic - sequence

The formula for an arithmetic sequence is $f(n)=a_1+(n - 1)d$, where $a_1$ is the first term and $d$ is the common difference. Here, $a_1 = 0.50$ and $d = 0.15$.

Step3: Substitute the values into the formula

[ \begin{align*} f(n)&=0.50+(n - 1)\times0.15\ &=0.50+0.15n-0.15\ &=0.15n + 0.35 \end{align*} ]

Answer:

$f(n)=0.15n + 0.35$