document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=254425>Question 254425</A>: <I><SPAN STYLE=\"word-break: break-all;\"> [Exponential functions]\r<BR>\n" );
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document.write( "A computer valued at $6500 depreciates at the rate of 14.3% per year.\r<BR>\n" );
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document.write( "I need to write a function that models the value of the computer and find the value of the computer after three years.\r<BR>\n" );
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document.write( "At first I wrote y=6500(1.143)^x as the function, but when I checked in the back of the textbook, it said y=6500(0.857)^x. How did they get that number?\r<BR>\n" );
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document.write( "Thank you! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #186734 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=186734\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> it depreciates at the rate of 14.3% per year.\r<BR>\n" );
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document.write( "this means that the value drops by 14.3% per year.\r<BR>\n" );
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document.write( "14.3% / 100% = .143\r<BR>\n" );
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document.write( "your equation increased the value by 14.3% per year.\r<BR>\n" );
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document.write( "you added .1453*6500 to 6500 to get:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6500+%2B+%286500+%2A+.143%29 ALIGN=MIDDLE  ALT=\"6500+%2B+%286500+%2A+.143%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "when you factor out the 6500, you get:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6500+%2A+%281+%2B+.143%29 ALIGN=MIDDLE  ALT=\"6500+%2A+%281+%2B+.143%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6500+%2A+1.143 ALIGN=MIDDLE  ALT=\"6500+%2A+1.143\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "that does it for one year.\r<BR>\n" );
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document.write( "for n years, you then raised to the exponent of n to get:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6500+%2A+1.143%5En ALIGN=MIDDLE  ALT=\"6500+%2A+1.143%5En\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "your equation should have the decreased the value by 14.3% per year.\r<BR>\n" );
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document.write( "you needed to subtract .143*6500 from 6500 to get:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6500+-+%286500+%2A+.143%29 ALIGN=MIDDLE  ALT=\"6500+-+%286500+%2A+.143%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "when you factor out the 6500, you get:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6500+%2A+%281+-+.143%29 ALIGN=MIDDLE  ALT=\"6500+%2A+%281+-+.143%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6500+%2A+.857 ALIGN=MIDDLE  ALT=\"6500+%2A+.857\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "that does it for one year.\r<BR>\n" );
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document.write( "for n years, you then raised to the exponent of n to get:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6500+%2A+.857%5En ALIGN=MIDDLE  ALT=\"6500+%2A+.857%5En\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "where you used x, I used n.   \r<BR>\n" );
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document.write( "if you prefer to use x, just replace n with x.\r<BR>\n" );
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document.write( "graph of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+6500+%2A+%281.143%29%5Ex ALIGN=MIDDLE  ALT=\"y+=+6500+%2A+%281.143%29%5Ex\"   DISABLED_style= \"max-width:90%; height:auto;\" > looks like this.\r<BR>\n" );
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document.write( "the y values of the graph are in hundreds.\r<BR>\n" );
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document.write( "6000 = 60<BR>\n" );
document.write( "7000 = 70<BR>\n" );
document.write( "6500 = 65, etc.\r<BR>\n" );
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document.write( "the only x values you are interested are when x is positive.\r<BR>\n" );
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document.write( "those values are to the right of the y-axis which is the vertical line when x = 0.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph+%28400%2C400%2C-1%2C10%2C-20%2C200%2C65%2A%281.143%29%5Ex%29 ALIGN=MIDDLE  ALT=\"graph+%28400%2C400%2C-1%2C10%2C-20%2C200%2C65%2A%281.143%29%5Ex%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "you can see that as x increases, the value of y increases.\r<BR>\n" );
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document.write( "graph of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+6500+%2A+%28.857%29%5Ex ALIGN=MIDDLE  ALT=\"y+=+6500+%2A+%28.857%29%5Ex\"   DISABLED_style= \"max-width:90%; height:auto;\" > looks like this.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph+%28400%2C400%2C-1%2C10%2C-20%2C200%2C65%2A%28.857%29%5Ex%29 ALIGN=MIDDLE  ALT=\"graph+%28400%2C400%2C-1%2C10%2C-20%2C200%2C65%2A%28.857%29%5Ex%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "you can see that as x increases, the value of y decreases.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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