document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1008550>Question 1008550</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In the year 2000, Anna bought a new car for $26,000.  In 2005, she was told that the value of her car was $15,000 due to depreciation.  She is told that the value of her car depreciates linearly.\r<BR>\n" );
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document.write( "a) Find a function V(t) which gives the value of the car t years after the year 2000<BR>\n" );
document.write( "b) In 2008, Anna is told that she will be given $7,000 for her car if she decides to trade it in for a new car.  Use the function from part (a) above to determine the value of her car in 2008.<BR>\n" );
document.write( "c) Is the $7,000 value fair based on what she was told about the linear depreciation?<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 #627324 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=627324\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> year 2000 car is bought for 26,000.<BR>\n" );
document.write( "year 2005, value of car is 15,000.\r<BR>\n" );
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document.write( "let x = 0 represent the year 2000<BR>\n" );
document.write( "then x = 5 represents the year 2005<BR>\n" );
document.write( "then x = 8 represents the year 2008\r<BR>\n" );
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document.write( "y = mx + b is the slope intercdept form of a straight line.\r<BR>\n" );
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document.write( "y = value of the car.<BR>\n" );
document.write( "x = year<BR>\n" );
document.write( "m is the slope of the change in the value of y divided by the change in the value of x.<BR>\n" );
document.write( "b is the y-intercept which is the value of y when the value of x is 0.\r<BR>\n" );
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document.write( "when x = 0, y = 26,000<BR>\n" );
document.write( "when x = 5, y = 15,000\r<BR>\n" );
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document.write( "the slope is equal to (y2-y1)/(x2-x1)\r<BR>\n" );
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document.write( "y2 = 15,000<BR>\n" );
document.write( "y1 = 26,000<BR>\n" );
document.write( "x2 = 5<BR>\n" );
document.write( "x1 = 0\r<BR>\n" );
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document.write( "slope = (15,000 - 26,000) / (5 - 0) = -11,000 / 5 = -2,200.\r<BR>\n" );
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document.write( "this means that the car is losing value by 2,2000 per year.\r<BR>\n" );
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document.write( "y = mx + b becomes y = -2,200 * x + b\r<BR>\n" );
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document.write( "b is the value of y when x is equal to 0 which is the value of the car when it was brand new.\r<BR>\n" );
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document.write( "b is therefore equal to 26,000 and the equation is therefore equal to:\r<BR>\n" );
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document.write( "y = -2,200 * x + 26,000\r<BR>\n" );
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document.write( "in year 0, the car is worth 26,000.<BR>\n" );
document.write( "in year 5, the car is worth 26,000 - 2,200 * 5 = 15,000.<BR>\n" );
document.write( "in year 8, the car is worth 26,000 - 2,200 * 8 = 8,400.\r<BR>\n" );
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document.write( "the offer of 7,000 is 1,400 dollar below the remaining value of the car based on straight line depreciation.\r<BR>\n" );
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document.write( "you can see this graphically below:\r<BR>\n" );
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document.write( "the first picture shows x = 0 and x = 5<BR>\n" );
document.write( "the value at x = 0 is 26,000<BR>\n" );
document.write( "the vlaue at x = 5 is 15,000<BR>\n" );
document.write( "this is based on loss of value of 2,200 per year based on straight line depreciation.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2015/122703.jpg\" alt=\"$$$\" </>\r<BR>\n" );
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document.write( "the second picture shows x = 5 and x = 8.<BR>\n" );
document.write( "the value at x = 5 is 15,000<BR>\n" );
document.write( "the value at x = 8 is 8,400<BR>\n" );
document.write( "you can also see the offer of 7,000 at x = 8.<BR>\n" );
document.write( "it is below the value of 8,400.<BR>\n" );
document.write( "the difference is 1,400.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2015/122704.jpg\" alt=\"$$$\" </>\r<BR>\n" );
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document.write( "the red line is the value of the car in year x.<BR>\n" );
document.write( "the blue line is the value of the offer in year x.\r<BR>\n" );
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document.write( "the actual year is 2000 + x.\r<BR>\n" );
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document.write( "when x is 0, the year is 2000<BR>\n" );
document.write( "when x is 5, the year is 2005<BR>\n" );
document.write( "when x is 8, the year is 2008\r<BR>\n" );
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