In 2003 there were 1078 JC Penney stores and in 2007 there were 1067 stores.(a) Write a linear equation that gives the number of stores (S) in terms of of the year(1). Let 1=3 represent2003.(b) Use your equation to predict the number of stores for the year 2012 and 2014.(c) Are you answers reasonable? ​

Answer:a) [tex]f(s)=\frac{-11}{3}s+\frac{3245}{3}[/tex] [tex]f(1)=1078 stores[/tex] b) 2012, 1049 stores. 2014, 1041 stores. c) Yes it is a downsizing company.Step-by-step explanation:a)s=year | f(s) = number of stores per year1 | 10784| 1067[tex]m=\frac{1067-1078}{4-1}\Rightarrow m=\frac{-11}{3}\\1078=-\frac{11}{3}*1+b\Rightarrow b=\frac{3245}{3}\\f(s)=\frac{-11}{3}s+\frac{3245}{3}[/tex]s=1 in 2003[tex]s=1 year =2003\\ Testing\\f(1)=\frac{-11}{3}(1)+\frac{3245}{3}=\frac{3234}{3}=1078\\ f(1)=1078[/tex]b) For 2012, s=9. For 2014, s=11[tex]\\f(s)=\frac{-11}{3}s+\frac{3245}{3}\\ \\f(9)=\frac{-11}{3}(9)+\frac{3245}{3}\cong1049\\\\f(11)=\frac{-11}{3}(11)+\frac{3245}{3}\cong=1041[/tex]c) In deed. Since the function shows a decreasing amount of JC Penney stores. Maybe this is a downsizing from this company, progressively closing some stores.