document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=65473>Question 65473</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Stereo System.  You purchase a stereo system for $830. After a 3-month trial period, the value of the stereo system decreases 13% each year.\r<BR>\n" );
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document.write( "a.	Write an exponential decay model for the value of the stereo system in terms of the number of years since the purchase.<BR>\n" );
document.write( "b.      What was the value of the system after 1 year?\r<BR>\n" );
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document.write( "I thought it was 830(.87)^x... but how do I put in the model the part about it only starts decreasing AFTER  3 months??? \r<BR>\n" );
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document.write( "Thanks very much,<BR>\n" );
document.write( "E </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #46015 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=46015\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V%5BT%5D+=+P%281+-+r%29%5ET ALIGN=MIDDLE  ALT=\"V%5BT%5D+=+P%281+-+r%29%5ET\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V%5BT%5D ALIGN=MIDDLE  ALT=\"V%5BT%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the value after T years<BR>\n" );
document.write( "P is the purchase price<BR>\n" );
document.write( "r is the annual interest rate<BR>\n" );
document.write( "T is number of years after the 3 month trial period<BR>\n" );
document.write( "Note that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=T+%3E=+0 ALIGN=MIDDLE  ALT=\"T+%3E=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=T+=+0 ALIGN=MIDDLE  ALT=\"T+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > is when the <BR>\n" );
document.write( "3 month trial period has ended<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=T ALIGN=MIDDLE  ALT=\"T\"   DISABLED_style= \"max-width:90%; height:auto;\" >(years) = (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t ALIGN=MIDDLE  ALT=\"t\"   DISABLED_style= \"max-width:90%; height:auto;\" >(months) - 3) / 12<BR>\n" );
document.write( "Note that when <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+3 ALIGN=MIDDLE  ALT=\"t+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, T = 0 and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V%28T%29+=+P%281+-+r%29%5ET+=+P ALIGN=MIDDLE  ALT=\"V%28T%29+=+P%281+-+r%29%5ET+=+P\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "as it should.<BR>\n" );
document.write( "When <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+15 ALIGN=MIDDLE  ALT=\"t+=+15\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=T+=+1 ALIGN=MIDDLE  ALT=\"T+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" > (1 year after trial)<BR>\n" );
document.write( "and V(1) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=830%28.87%29 ALIGN=MIDDLE  ALT=\"830%28.87%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "V(1) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=722.10 ALIGN=MIDDLE  ALT=\"722.10\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "What is the value after 1 year? I assume this means 1 year after<BR>\n" );
document.write( "purchase, not 1 year after the 3 month trial.<BR>\n" );
document.write( "Set <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+12 ALIGN=MIDDLE  ALT=\"t+=+12\"   DISABLED_style= \"max-width:90%; height:auto;\" > then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=T+=+%2812+-+3%29+%2F+12 ALIGN=MIDDLE  ALT=\"T+=+%2812+-+3%29+%2F+12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=T+=+9+%2F+12 ALIGN=MIDDLE  ALT=\"T+=+9+%2F+12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=T+=+3%2F4 ALIGN=MIDDLE  ALT=\"T+=+3%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "V(3/4) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+830%281+-+.13%29%5E%283%2F4%29 ALIGN=MIDDLE  ALT=\"+830%281+-+.13%29%5E%283%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "V(3/4) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=830%28.87%29%5E%283%2F4%29 ALIGN=MIDDLE  ALT=\"830%28.87%29%5E%283%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "V(3/4) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=830+%2A+.900 ALIGN=MIDDLE  ALT=\"830+%2A+.900\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "V(3/4) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=747.68 ALIGN=MIDDLE  ALT=\"747.68\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So, the value after a year is $ 747.68 </SPAN>\n" );
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