Respuesta :
Answer:
C. [tex]f(n)=0.15n+0.35[/tex]
Step-by-step explanation:
We have been given a sequence representing the 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, ...
An arithmetic sequence is in form [tex]a_n=a_1+(n-1)d[/tex], where [tex]a_n[/tex]= nth term of sequence.
[tex]a_1[/tex]= 1st term of the sequence.
d= Common difference.
We can see from our sequence that 1st term of our sequence is 0.50.
Let us find common difference by subtracting 0.50 from 0.65.
[tex]\text{Common difference}=0.65-0.50=0.15[/tex]
Upon substituting our values in arithmetic sequence we will get,
[tex]f(n)=0.50+(n-1)0.15[/tex]
Upon distributing 0.15 we will get,
[tex]f(n)=0.50+0.15n-0.15[/tex]
Now let us combine like terms.
[tex]f(n)=0.15n+0.50-0.15[/tex]
[tex]f(n)=0.15n+0.35[/tex]
Therefore, the equation [tex]f(n)=0.15n+0.35[/tex] will represent Marisa’s library fine as a function of a book that is n days overdue and option C is the correct choice.
