document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=33420>Question 33420</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 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.<BR>\n" );
document.write( "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??<BR>\n" );
document.write( "N(t)=________________<BR>\n" );
document.write( "In 2007:_____________<BR>\n" );
document.write( "0 stores in:_________\r<BR>\n" );
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document.write( "This is from a worksheet, not my book. I would GREATLY appreciate any and all help received. Thanks again! : )  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #19765 by </B><A HREF=/tutors/aboutme.mpl?userid=longjonsilver><B>longjonsilver(2297)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=longjonsilver><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=longjonsilver><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=19765\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> YEAR _t _N<BR>\n" );
document.write( "1992 _0 4032<BR>\n" );
document.write( "2002 10 3682\r<BR>\n" );
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document.write( "First thing is to assume a linear relationship rather than some sort of curve.\r<BR>\n" );
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document.write( "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.\r<BR>\n" );
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document.write( "We can find c straightaway: when t=0, N=4032, so from N=mt+c we get<BR>\n" );
document.write( "4032 = m(0) + c<BR>\n" );
document.write( "--> c = 4032\r<BR>\n" );
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document.write( "so we have N=mt+4032\r<BR>\n" );
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document.write( "Now for the gradient:<BR>\n" );
document.write( "gradient, m = (change in y)/(change in x)<BR>\n" );
document.write( "m = (3682-4032)/(10-0)<BR>\n" );
document.write( "m = -350/10<BR>\n" );
document.write( "m = -35\r<BR>\n" );
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document.write( "--> N = -35t+4032\r<BR>\n" );
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document.write( "In 2007, t = 15, so N = -35(15)+4032<BR>\n" );
document.write( "N = -525+4032<BR>\n" );
document.write( "N = 3507 stores\r<BR>\n" );
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document.write( "No stores is when N=0, so 0 = -35t+4032<BR>\n" );
document.write( "35t = 4032<BR>\n" );
document.write( "t = 115.2<BR>\n" );
document.write( "so after 116 years, so in year 2108, if the number of closures followed the same rate.\r<BR>\n" );
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document.write( "jon.<BR>\n" );
document.write( " </SPAN>\n" );
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