Question

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 1

a)
`f(s)=(-11)/(3)s+(3245)/(3)`
`f(1)=1078 stores` b) 2012, 1049 stores. 2014, 1041 stores. c) Yes it is a downsizing company.

Explanation:

a)

s=year | f(s) = number of stores per year

1 | 1078

4| 1067

`m=(1067-1078)/(4-1)\Rightarrow m=(-11)/(3)\\1078=-(11)/(3)*1+b\Rightarrow b=(3245)/(3)\\f(s)=(-11)/(3)s+(3245)/(3)`

s=1 in 2003

`s=1 year =2003\\ Testing\\f(1)=(-11)/(3)(1)+(3245)/(3)=(3234)/(3)=1078\\ f(1)=1078`

b) For 2012, s=9. For 2014, s=11

`\\f(s)=(-11)/(3)s+(3245)/(3)\\ \\f(9)=(-11)/(3)(9)+(3245)/(3)\cong1049\\\\f(11)=(-11)/(3)(11)+(3245)/(3)\cong=1041`

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.