document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1100351>Question 1100351</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A pair of women's running shoes cost $110 in 2004 and the same shoes cost $130 in 2009 due to inflation.<BR>\n" );
document.write( "a. Develop an exponential model to describe the rate of inflation over this time period.<BR>\n" );
document.write( "b. If inflation continues at the same; rate, use your model in part; (a) to estimate the price of the shoes in 2016.<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #714848 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=714848\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> shoes cost 110 in 2004.<BR>\n" );
document.write( "same shoes cost 130 in 2009.\r<BR>\n" );
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document.write( "2009 - 2004 = 5<BR>\n" );
document.write( "130 = 110 * (1 + r) ^ 5<BR>\n" );
document.write( "divide both sides of the equation by 110 to get:<BR>\n" );
document.write( "130/110 = (1 + r) ^ 5<BR>\n" );
document.write( "take the fifth root of both sides of the equation to get:<BR>\n" );
document.write( "(130/110)^(1/5) = 1 + r<BR>\n" );
document.write( "solve for r to get:<BR>\n" );
document.write( "r = (130/110)^(1/5) - 1 = .033975227\r<BR>\n" );
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document.write( "that's your average annual exponential growth rate of inflation.\r<BR>\n" );
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document.write( "in 2009, at the present rate of inflation from 2004, the shoes will cost 110 * (1.033975227) ^ 5 = 130.\r<BR>\n" );
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document.write( "in 2016, at the present rate of inflation from 2004, the shoes will cost (110 * (1.033975227) ^ 12 = 164.2533691\r<BR>\n" );
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document.write( "2009 is 5 years from 2004.<BR>\n" );
document.write( "2016 is 12 years from 2004.\r<BR>\n" );
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document.write( "graphically, the equation looks like this:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2017/110601.jpg\" alt=\"$$$\" >\r<BR>\n" );
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