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?

Question

14-11-2019
Mathematics

contestada

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?

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profantoniofonte profantoniofonte · Answer 1 · 2019-11-16T03:36:33+01:00

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 year

1 | 1078

4| 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.