document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=755955>Question 755955</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me understand the following equation:\r<BR>\n" );
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document.write( "V=A(1-K^-t/T) for K.\r<BR>\n" );
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document.write( "I understand / both sides by A then subtracting both sides by 1. What to do with the -K? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #459925 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=459925\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the interpretation of this problem is now:\r<BR>\n" );
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document.write( "V = A * (1 - K<sup>(-t/T)</sup>)\r<BR>\n" );
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document.write( "divide both sides of this equation by A to get:\r<BR>\n" );
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document.write( "V/A = 1 - K<sup>(-t/T)</sup>\r<BR>\n" );
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document.write( "subtract 1 from both sides of the equation to get:\r<BR>\n" );
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document.write( "V/A - 1 = -K<sup>(-t/T)</sup>\r<BR>\n" );
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document.write( "multiply both sides of the equation by -1 to get:\r<BR>\n" );
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document.write( "1 - V/A = K<sup>(-t/T)</sup>\r<BR>\n" );
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document.write( "this becomes:\r<BR>\n" );
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document.write( "1 - V/A = 1 / K<sup>(t/T)</sup>\r<BR>\n" );
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document.write( "multiply both sides of this equation by K<sup>(t/T)</sup>) and divide both sides of this equation by (1 - V/A) to get:\r<BR>\n" );
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document.write( "K<sup>(t/T)</sup>) = 1 / (1 - V/A)\r<BR>\n" );
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document.write( "raise both sides of the equation by the power of T to get:\r<BR>\n" );
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document.write( "(K<sup>(t/T)</sup>)<sup>T</sup> = (1 / (1 - V/A))<sup>T</sup>\r<BR>\n" );
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document.write( "simplify this to get:\r<BR>\n" );
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document.write( "K<sup>(t)</sup> = (1 / (1 - V/A))<sup>T</sup>\r<BR>\n" );
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document.write( "take the t root of both sides of the equation to get:\r<BR>\n" );
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document.write( "((K<sup>(t)</sup>)<sup>(1/t)</sup> = ((1 / (1 - V/A))<sup>T</sup>)<sup>(1/t)</sup>\r<BR>\n" );
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document.write( "simplify to get:\r<BR>\n" );
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document.write( "K = ((1 / (1 - V/A))<sup>T</sup>)<sup>(1/t)</sup>\r<BR>\n" );
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document.write( "which can also be written as:\r<BR>\n" );
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document.write( "K = root(t,((1 / (1 - V/A))<sup>T</sup>))\r<BR>\n" );
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document.write( "which looks like this:\r<BR>\n" );
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document.write( "K = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=root%28t%2C%281+%2F+%281+-+V%2FA%29%29%5ET%29 ALIGN=MIDDLE  ALT=\"root%28t%2C%281+%2F+%281+-+V%2FA%29%29%5ET%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "the answer has been confirmed to be correct.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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