document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1097601>Question 1097601</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A manufacturer buys a new machine costing $130,000. It is estimated that the machine has a useful lifetime of fifteen years and a salvage value of $4000 at that time.<BR>\n" );
document.write( "(a) Find a formula for the value of the machine after t years, where 0 &#8804; t &#8804; 15.<BR>\n" );
document.write( "V(t) =\r<BR>\n" );
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document.write( "(b) Find the value of the machine after ten years.<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 #712183 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=712183\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> i believe it works like this.\r<BR>\n" );
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document.write( "the value today is 130,000<BR>\n" );
document.write( "the value in 15 years is 4000.\r<BR>\n" );
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document.write( "with straigh line depreciation, the decrease in value each year is calculated using the formula:\r<BR>\n" );
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document.write( "y = mx + b.\r<BR>\n" );
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document.write( "m is the slope and b is the y-intercept.\r<BR>\n" );
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document.write( "the y-intercept is the value of y when x = 0.\r<BR>\n" );
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document.write( "that would be 130,000 which is the value of the machine when it is bought.\r<BR>\n" );
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document.write( "therefore the equation becomes:\r<BR>\n" );
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document.write( "y = mx + 130,000.\r<BR>\n" );
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document.write( "the formula for the slope is m = (y2 - y1) / (x2 - x1)\r<BR>\n" );
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document.write( "(x1,y1) is equal to 0, 130,000)\r<BR>\n" );
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document.write( "(x2,y2) is equal to (15, 4,000)\r<BR>\n" );
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document.write( "m becomes equal to (4,000 - 130,000) / (15 - 0) = -136,000 / 15 = -8400.\r<BR>\n" );
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document.write( "formula becomes y = -8400 * x + 130,000\r<BR>\n" );
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document.write( "when x = 0, y = 130,000<BR>\n" );
document.write( "when x = 15, y = 4,000.\r<BR>\n" );
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document.write( "a graph of that equation is shown below showing the value of the machine after 10 years.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src= \"http://theo.x10hosting.com/2017/101611.jpg\" alt=\"$$$\" >\r<BR>\n" );
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document.write( "that value is 46000 because y = -8400 * x + 130,000 becomes y = -8400 * 10 + 130,000 when x = 10 which becomes y = -84000 + 130,000 which becomes y = 46,000.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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