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Question 33420: Not sure if the subject is right...this is a function word problem. I think I know the answer, but don't know how to write a function for it. PLEASE HELP! Thanks.
In 1992, there were 4,032 Ace Hardware Stores, while that number had decreased to 3,682 in 2002. Write a function that represents the number of stores, N, in terms of the year, letting t=0 represent the year 1992. Then use your function to predict the number of stores that will exist in the year 2007. Theoretically, in what year will there be NO Ace Hardware stores left??
N(t)=________________
In 2007:_____________
0 stores in:_________
This is from a worksheet, not my book. I would GREATLY appreciate any and all help received. Thanks again! : )
Answer by longjonsilver(2297)   (Show Source):
You can put this solution on YOUR website! YEAR _t _N
1992 _0 4032
2002 10 3682
First thing is to assume a linear relationship rather than some sort of curve.
This will be of the form y=mx+c or with our variables N=mt+c. We need to find the gradient m and the y-intercept, c.
We can find c straightaway: when t=0, N=4032, so from N=mt+c we get
4032 = m(0) + c
--> c = 4032
so we have N=mt+4032
Now for the gradient:
gradient, m = (change in y)/(change in x)
m = (3682-4032)/(10-0)
m = -350/10
m = -35
--> N = -35t+4032
In 2007, t = 15, so N = -35(15)+4032
N = -525+4032
N = 3507 stores
No stores is when N=0, so 0 = -35t+4032
35t = 4032
t = 115.2
so after 116 years, so in year 2108, if the number of closures followed the same rate.
jon.
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