document.write( "Question 1163792: A piece of machinery is purchased for $400,000. Accountants have decided to
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\n" ); document.write( "after 10 years. Letting V equal the book value of the machine;
\n" ); document.write( "a) Assuming that there is no salvage value, determine the function V=f(t).\r
\n" ); document.write( "\n" ); document.write( "b) If the machine can be resold after 10 years for $25,000. Determine the
\n" ); document.write( "function V=f (t). \n" ); document.write( "
Algebra.Com's Answer #788000 by Edwin McCravy(20060)\"\" \"About 
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A piece of machinery is purchased for $400,000. Accountants have decided to
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document.write( "That means we have the equation of a line of the form y=mx+b, except we\r\n" );
document.write( "change the letters to V = mt+b, and that when t=0, V=400000. In other words,\r\n" );
document.write( "the line begins at the point (t,V) = (0,400000), and we can substitute 0 for\r\n" );
document.write( "t and 400000 for V and get:\r\n" );
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document.write( "     V = mt+b\r\n" );
document.write( "400000 = m∙(0)+b\r\n" );
document.write( "400000 = 0+b\r\n" );
document.write( "400000 = b\r\n" );
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document.write( "We now know what b is.  So the formula is now\r\n" );
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document.write( "     V = mt+400000\r\n" );
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\n" ); document.write( "with machine being fully depreciated after 10 years.
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\r\n" );
document.write( "That means that when t=10 years, the value V is 0 (it is worthless).\r\n" );
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document.write( "So the line ends at the point where t=10 and V=0, which is the point (10,0).\r\n" );
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document.write( "We substitute that point in the equation\r\n" );
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document.write( "      V = mt+400000\r\n" );
document.write( "      0 = m∙(10)+400000\r\n" );
document.write( "-400000 = 10m\r\n" );
document.write( " -40000 = m\r\n" );
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document.write( "So now we know m. so we substitute -40000 for m and we have:\r\n" );
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document.write( "      V = mt+4000000\r\n" );
document.write( "      V = -40000t+4000000\r\n" );
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document.write( "Letting V equal the book value of the machine [at time t anywhere between\r\n" );
document.write( "t=0 and t=10.]\r\n" );
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document.write( "Which we did.\r\n" );
document.write( "

\n" ); document.write( "a) Assuming that there is no salvage value, determine the function V=f (t).
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\r\n" );
document.write( "We just did. \"No salvage value\" and \"fully depreciated\" mean the same thing.    So\r\n" );
document.write( "    V = -40000t+400000   [answer to (a) part)]\r\n" );
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\n" ); document.write( "b) If the machine can be resold after 10 years for $25,000. Determine the
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\r\n" );
document.write( "We go back to what we had just before we were told that is was worthless\r\n" );
document.write( "when t=10 years.  It is no longer assumed worthless when t=10 years, for now\r\n" );
document.write( "it is worth 25000 when t=10 years.  The formula before we assumed it was\r\n" );
document.write( "worthless when t=10, was this.\r\n" );
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document.write( "     V = mt+400000\r\n" );
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document.write( "Now when t=10, V=25000, [not 0], so the line now ends at the point\r\n" );
document.write( "(10,25000).\r\n" );
document.write( "So we substitute t=10 and V = 25000\r\n" );
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document.write( "  25000 = m∙(10)+400000\r\n" );
document.write( "  25000 = 10m+400000\r\n" );
document.write( "-375000 = 10m\r\n" );
document.write( " -37500 = m\r\n" );
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document.write( "Now we know m, so we substitute -37500 for m and we have:\r\n" );
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document.write( "      V = mt+4000000\r\n" );
document.write( "      V = -37500t+4000000   [answer to (b) part]\r\n" );
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document.write( "Edwin
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