document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=628699>Question 628699</A>: <I><SPAN STYLE=\"word-break: break-all;\"> An exponential decay graph shows the expected depreciation for a new boat, selling for $3,500, over 10 years.\r<BR>\n" );
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document.write( "a.  Write an exponential function for the graph.\r<BR>\n" );
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document.write( "b.  Use the function in part a to find the value of the boat after 9.5 years. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #395848 by </B><A HREF=/tutors/aboutme.mpl?userid=jsmallt9><B>jsmallt9(3758)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jsmallt9><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=395848\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> First, this problem has nothing to do with Trigonometry. It belongs in one of the categories related to exponents. Please post using a possibly relevant category.<br><BR>\n" );
document.write( "Second, without the graph you were given it will be impossible for a tutor to solve this problem. I will, nevertheless, try to help as much as I can.<br><BR>\n" );
document.write( "The general equation for exponential growth and decay is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+=+A%5B0%5D%2A%281%2Br%29%5Et ALIGN=MIDDLE  ALT=\"A+=+A%5B0%5D%2A%281%2Br%29%5Et\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "where<BR>\n" );
document.write( "t is a number of units of time. (Often the units are years so t would be a number of years.)<BR>\n" );
document.write( "A = the amount after \"t\" units of time.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5B0%5D ALIGN=MIDDLE  ALT=\"A%5B0%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the starting amount (IOW the amount at t = 0. This is why the A has a subscript of zero.)<BR>\n" );
document.write( "r is a decimal (or fraction) between 0 and 1 which represents the rate of change. A positive r means growth. A negative r means decay. (Note: Some books use <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+=+A%5B0%5D%2Ar%5Et ALIGN=MIDDLE  ALT=\"A+=+A%5B0%5D%2Ar%5Et\"   DISABLED_style= \"max-width:90%; height:auto;\" >, merging the 1 and r. In this case if r > 1 then the equation is for growth and if r is between 0 and 1 then the equation is for decay. I prefer the first form I gave you because that percent growths or decays are easier to use with that form.)<br><BR>\n" );
document.write( "You have been given the original amount, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5B0%5D ALIGN=MIDDLE  ALT=\"A%5B0%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >. So your equation so far is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+=+3500%2A%281%2Br%29%5Et ALIGN=MIDDLE  ALT=\"A+=+3500%2A%281%2Br%29%5Et\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "From this point on I can only tell you what you should do to finish:<ol><li>Find the value for r:<ol><li>Look at the graph and find the coordinates of any point (other than where t = 0) on the graph. (If the axes are not labeled t and A, then the \"t\" in the equation corresponds to \"x\" and the \"A\" corresponds to the \"y\".)</li><li>Replace the t and A in your equation with the coordinates you found in step 1.</li><li>Solve this equation for r.</li></ol></li><li>Rewrite your working equation:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+=+3500%2A%281%2Br%29%5Et ALIGN=MIDDLE  ALT=\"A+=+3500%2A%281%2Br%29%5Et\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "substituting in the value for r you just found. This (or the equation you get if you add the 1 to r) is the answer to part a.</li><li>Using the equation from part a, replace the t with 9.5 and solve for A. This will be the answer for part b.</li></ol><BR>\n" );
document.write( "Here's an example:<BR>\n" );
document.write( "1. Solve for r<BR>\n" );
document.write( "1.1 Find a point. Suppose that your graph shows that at t (or x) = 10, the A (or y) is 700.<BR>\n" );
document.write( "1.2 Insert the coordinates into your working equation:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=700+=+3500%2A%281%2Br%29%5E10 ALIGN=MIDDLE  ALT=\"700+=+3500%2A%281%2Br%29%5E10\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "1.3. Solve for r.<BR>\n" );
document.write( "Dividing both sides by 3500:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.2+=+%281%2Br%29%5E10 ALIGN=MIDDLE  ALT=\"0.2+=+%281%2Br%29%5E10\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "Find the 10th root of each side. (On your calculator use 0.2^(1/10) or 0.2^0.1)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.85133992+=+1+%2B+r ALIGN=MIDDLE  ALT=\"0.85133992+=+1+%2B+r\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Subtract 1 from each side:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-0.14866008+=+r ALIGN=MIDDLE  ALT=\"-0.14866008+=+r\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(BTW: As a percent, r is an approximately 15% rate of decay.)<br><BR>\n" );
document.write( "2. Replace the r in your working equation:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+=+3500%2A%281%2B-0.14866008%29%5Et ALIGN=MIDDLE  ALT=\"A+=+3500%2A%281%2B-0.14866008%29%5Et\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "This, or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+=+3500%2A%280.85133992%29%5Et ALIGN=MIDDLE  ALT=\"A+=+3500%2A%280.85133992%29%5Et\"   DISABLED_style= \"max-width:90%; height:auto;\" >, would be the answer to part a.<br><BR>\n" );
document.write( "3. To find the value of the car after 9.5, replace the t in you equation with 9.5 and solve for A:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+=+3500%2A%281%2B-0.14866008%29%5E%289.5%29 ALIGN=MIDDLE  ALT=\"A+=+3500%2A%281%2B-0.14866008%29%5E%289.5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Simplifying...<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+=+3500%2A%280.85133992%29%5E%289.5%29 ALIGN=MIDDLE  ALT=\"A+=+3500%2A%280.85133992%29%5E%289.5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Using 0.85133992^(9.5) on our calculators:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+=+3500%2A0.21675967 ALIGN=MIDDLE  ALT=\"A+=+3500%2A0.21675967\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+=+758.65884937 ALIGN=MIDDLE  ALT=\"A+=+758.65884937\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So after 9.5 years the car would be worth approximately $758.69. </SPAN>\n" );
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