document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1087074>Question 1087074</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The depreciated value VV of a machine is a linear function of time t in years. A machine that is purchased for $100000 today will be worth approximately $67681 in 33 years. Write the linear function V(t) that represents the value of the machine at a given time t.\r<BR>\n" );
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document.write( "     My work---> 100,1000---->67,681 3yrs <BR>\n" );
document.write( "67,681v+3=100,000 this is what I got but I'm not sure.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #701359 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=701359\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=\"black\" face=\"times\" size=\"3\">I think you meant to say \"The depreciated value V\" instead of \"The depreciated value VV\". I changed the VV to V. \r<BR>\n" );
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document.write( "The value today is V = 100000 dollars when the time is t = 0, which is the starting time value. <BR>\n" );
document.write( "The value in 33 years, when t = 33, is V = 67681 dollars\r<BR>\n" );
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document.write( "So we have two ordered pairs (0,100000) and (33,67681). I'm going to treat t as x, and treat V as y. So each ordered pair goes from the form (t,V) to (x,y). Using the (x,y) form we can use the slope formula\r<BR>\n" );
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document.write( "First point = (x1,y1) = (0,100000)<BR>\n" );
document.write( "Second point = (x2,y2) = (33,67681)<BR>\n" );
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;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m+=+%2867681+-+100000%29%2F%2833+-+0%29 ALIGN=MIDDLE  ALT=\"m+=+%2867681+-+100000%29%2F%2833+-+0%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m+=+%28-32319%29%2F%2833%29 ALIGN=MIDDLE  ALT=\"m+=+%28-32319%29%2F%2833%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m+=+-10773%2F11 ALIGN=MIDDLE  ALT=\"m+=+-10773%2F11\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m+=+-979.3636 ALIGN=MIDDLE  ALT=\"m+=+-979.3636\"   DISABLED_style= \"max-width:90%; height:auto;\" > Use a calculator here. The decimal form is approximate (the '36' portion repeats forever)\r<BR>\n" );
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document.write( "So the slope is roughly <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m+=+-979.3636 ALIGN=MIDDLE  ALT=\"m+=+-979.3636\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The y intercept is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b+=+100000 ALIGN=MIDDLE  ALT=\"b+=+100000\"   DISABLED_style= \"max-width:90%; height:auto;\" > because this is the starting value (at t = 0)\r<BR>\n" );
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document.write( "So we go from <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+mx%2Bb ALIGN=MIDDLE  ALT=\"y+=+mx%2Bb\"   DISABLED_style= \"max-width:90%; height:auto;\" > to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+-979.3636x%2B100000 ALIGN=MIDDLE  ALT=\"y+=+-979.3636x%2B100000\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The last thing to do is replace x with t and replace y with V(t) to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V%28t%29+=+-979.3636t%2B100000 ALIGN=MIDDLE  ALT=\"V%28t%29+=+-979.3636t%2B100000\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Therefore the value function is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V%28t%29+=+-979.3636t%2B100000 ALIGN=MIDDLE  ALT=\"V%28t%29+=+-979.3636t%2B100000\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "-------------------------------------------------\r<BR>\n" );
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document.write( "Let's check the function. Plug t = 0 into the function to get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V%28t%29+=+-979.3636t%2B100000 ALIGN=MIDDLE  ALT=\"V%28t%29+=+-979.3636t%2B100000\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V%280%29+=+-979.3636%2A0%2B100000 ALIGN=MIDDLE  ALT=\"V%280%29+=+-979.3636%2A0%2B100000\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V%280%29+=+0%2B100000 ALIGN=MIDDLE  ALT=\"V%280%29+=+0%2B100000\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V%280%29+=+100000 ALIGN=MIDDLE  ALT=\"V%280%29+=+100000\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So that matches with the fact the initial value is $100,000\r<BR>\n" );
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document.write( "Now plug in t = 33<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V%28t%29+=+-979.3636t%2B100000 ALIGN=MIDDLE  ALT=\"V%28t%29+=+-979.3636t%2B100000\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V%2833%29+=+-979.3636%2A%2833%29%2B100000 ALIGN=MIDDLE  ALT=\"V%2833%29+=+-979.3636%2A%2833%29%2B100000\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V%2833%29+=+-32318.9988%2B100000 ALIGN=MIDDLE  ALT=\"V%2833%29+=+-32318.9988%2B100000\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V%2833%29+=+67681.0012 ALIGN=MIDDLE  ALT=\"V%2833%29+=+67681.0012\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V%2833%29+=+67681.00 ALIGN=MIDDLE  ALT=\"V%2833%29+=+67681.00\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Which matches with the value after 33 years. So the answer is confirmed\r<BR>\n" );
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document.write( "Side Note: if you use the fraction form for the slope then you won't run into rounding errors. The fact that we're rounding to 2 decimal places means that we don't have to worry about precision too much as long as the slope is expressed to 3 decimal places or more. You're probably wondering what the slope means? If so, then the slope is simply the rate of value decay or drop. In this case, the slope -979.3636 means the value V(t) is decreasing by $979.36 each year. The actual drop is a bit more than that but you can only round to the nearest hundredth for money problems like this.</font> </SPAN>\n" );
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