document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=201383>Question 201383</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Problem2.<BR>\n" );
document.write( "High Tech Graphics bought a fax machine for $750. The fax machine depreciates at a rate of $25 a month.<BR>\n" );
document.write( "(a) Find a function F that can be used to determine the value of the fax machine t months after purchase.<BR>\n" );
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document.write( "F(t)=?<BR>\n" );
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document.write( "b) I need a graph of the function F(t)?<BR>\n" );
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document.write( "Thank you so much!!!!<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 #151611 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=151611\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let \r<BR>\n" );
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document.write( "x=time in months (ie t=0 means 0 months, t=1 means 1 month)\r<BR>\n" );
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document.write( "y=value of the machine\r<BR>\n" );
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document.write( "At first, the machine is $750. So at time x=0 the value of the machine is $750 which means that y=750. So we have one ordered pair (ie point) that is (0, 750).\r<BR>\n" );
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document.write( "After one month, the machine has lost $25 of its value. So after one month, the value of the machine is now $750-$25=$725 giving the values x=1 and y=725. So we have another ordered pair (point) of (1, 725)\r<BR>\n" );
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document.write( "a)\r<BR>\n" );
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document.write( "Now that we have two points (0, 750) and (1, 725), we can find the equation of the line that goes through them.\r<BR>\n" );
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document.write( "First let's find the slope of the line through the points <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left(0,750\right)\"> and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left(1,725\right)\">\r<BR>\n" );
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document.write( "Note: <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left(x_{1}, y_{1}\right)\"> is the first point <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left(0,750\right)\"> and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left(x_{2}, y_{2}\right)\"> is the second point <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left(1,725\right)\">.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29 ALIGN=MIDDLE  ALT=\"m=%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the slope formula.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=%28725-750%29%2F%281-0%29 ALIGN=MIDDLE  ALT=\"m=%28725-750%29%2F%281-0%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B2%5D=725 ALIGN=MIDDLE  ALT=\"y%5B2%5D=725\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B1%5D=750 ALIGN=MIDDLE  ALT=\"y%5B1%5D=750\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B2%5D=1 ALIGN=MIDDLE  ALT=\"x%5B2%5D=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D=0 ALIGN=MIDDLE  ALT=\"x%5B1%5D=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=%28-25%29%2F%281-0%29 ALIGN=MIDDLE  ALT=\"m=%28-25%29%2F%281-0%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=750 ALIGN=MIDDLE  ALT=\"750\"   DISABLED_style= \"max-width:90%; height:auto;\" > from <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=725 ALIGN=MIDDLE  ALT=\"725\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-25 ALIGN=MIDDLE  ALT=\"-25\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=%28-25%29%2F%281%29 ALIGN=MIDDLE  ALT=\"m=%28-25%29%2F%281%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" > from <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=-25 ALIGN=MIDDLE  ALT=\"m=-25\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce\r<BR>\n" );
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document.write( "So the slope of the line that goes through the points <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left(0,750\right)\"> and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left(1,725\right)\"> is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=-25 ALIGN=MIDDLE  ALT=\"m=-25\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now let's use the point slope formula:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-y%5B1%5D=m%28x-x%5B1%5D%29 ALIGN=MIDDLE  ALT=\"y-y%5B1%5D=m%28x-x%5B1%5D%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the point slope formula\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-750=-25%28x-0%29 ALIGN=MIDDLE  ALT=\"y-750=-25%28x-0%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=-25 ALIGN=MIDDLE  ALT=\"m=-25\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D=0 ALIGN=MIDDLE  ALT=\"x%5B1%5D=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B1%5D=750 ALIGN=MIDDLE  ALT=\"y%5B1%5D=750\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-750=-25x-25%280%29 ALIGN=MIDDLE  ALT=\"y-750=-25x-25%280%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-750=-25x%2B0 ALIGN=MIDDLE  ALT=\"y-750=-25x%2B0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-25x%2B0%2B750 ALIGN=MIDDLE  ALT=\"y=-25x%2B0%2B750\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add 750 to both sides. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-25x%2B750 ALIGN=MIDDLE  ALT=\"y=-25x%2B750\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms. \r<BR>\n" );
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document.write( "So the equation that goes through the points <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left(0,750\right)\"> and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left(1,725\right)\"> is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-25x%2B750 ALIGN=MIDDLE  ALT=\"y=-25x%2B750\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now replace the \"y\" with F(t) and the \"x\" with \"t\" to get the function <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=F%28t%29=-25t%2B750 ALIGN=MIDDLE  ALT=\"F%28t%29=-25t%2B750\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Answer:\r<BR>\n" );
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document.write( "So the function F that models the value of the fax machine is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=F%28t%29=-25t%2B750 ALIGN=MIDDLE  ALT=\"F%28t%29=-25t%2B750\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "b) \r<BR>\n" );
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document.write( "To graph ANY linear function, simply plot two points and draw a line through them (it's that simple). Since we already know that the function goes through the points (0, 750) and (1, 725), just plot these points and draw a line through them like so:\r<BR>\n" );
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document.write( "Note: the ticks on the x-axis are one unit apart. The x-axis is so far down below that it can't be shown (without distorting the graph).\r<BR>\n" );
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