A pool pass costs $30 for the first month and $15 each additional month. Construct an explicit rule in function notation to model the arithmetic sequence. F(n) = ___________ (simplfy your answer) Find F(12)
Accepted Solution
A:
Answer:[tex]F(n)=15(n+1)[/tex] [ where [tex]n[/tex] represents number of months][tex]F(12)=195[/tex]Step-by-step explanation:Pool pass cost for first month =$30Pool pass cost after first month = $15 for each monthThe total amount charged by the pool can be expressed as a function [tex]F(n)[/tex] where [tex]n[/tex] represents the number of months.[tex]F(n)=15(n-1)+30[/tex]This can be simplified by using distribution.[tex]F(n)=(15n-15)+30[/tex][tex]F(n)=15n-15+30[/tex][tex]F(n)=15n+15[/tex]Take 15 as greatest common factor.∴ [tex]F(n)=15(n+1)[/tex] For [tex]n=12[/tex] months we plugin 12 for [tex]n[/tex] in the function.[tex]F(12)=15(12+1)[/tex][tex]F(12)=15(13)[/tex][tex]F(12)=195[/tex]∴ Amount charged by pool for 12 months = $195