document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1078701>Question 1078701</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If P dollars invested in an account that earns interest at 7% compounded annually the amount available after t years is A=P(1+1.07)^t. How many years will it take for $16000 in this account to grow to $22400? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #693088 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=693088\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the formula is actually:\r<BR>\n" );
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document.write( "A = P * (1 + .07) ^ T\r<BR>\n" );
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document.write( "since 1 + .07 is equal to 1.07, the formula becomes:\r<BR>\n" );
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document.write( "A = P * 1.07 ^ T\r<BR>\n" );
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document.write( "replace P with 16,000 and replace A with 22,400 and the equation becoms:\r<BR>\n" );
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document.write( "22,400 = 16,000 * 1.07 ^ T\r<BR>\n" );
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document.write( "divide both sides of the equation by 16,000 to get:\r<BR>\n" );
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document.write( "22,400 / 16,000 = 1.07 ^ T\r<BR>\n" );
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document.write( "simplify to get:\r<BR>\n" );
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document.write( "1.4 = 1.07 ^ T\r<BR>\n" );
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document.write( "take the log of both sides of the equation to get:\r<BR>\n" );
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document.write( "log(1.4) = log(1.07 ^ T)\r<BR>\n" );
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document.write( "this is equivalent to:\r<BR>\n" );
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document.write( "log(1.4) = T * log(1.07)\r<BR>\n" );
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document.write( "divide both sides of the equation by log(1.07) to get:\r<BR>\n" );
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document.write( "log(1.4) / log(1.07) = T\r<BR>\n" );
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document.write( "solve for T to get T = 4.973085396\r<BR>\n" );
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document.write( "16,000 should grow to 22,400 in 4.973085396 years.\r<BR>\n" );
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document.write( "to confirm, replace T in the original equation to get:\r<BR>\n" );
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document.write( "22,400 = 16,000 * 1.07 ^ (4.973085396)\r<BR>\n" );
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document.write( "use your calculator to evalutat 16,000 * 1.07 ^ (4.973085396)\r<BR>\n" );
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document.write( "you will find that it is equal to 22,400, confirming the solution is correct.\r<BR>\n" );
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document.write( "the peoerty of logs that allows you to solve this equation is:\r<BR>\n" );
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document.write( "log(b^x) = x * log(b)\r<BR>\n" );
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document.write( "for example:\r<BR>\n" );
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document.write( "log(2^5) = 5 * log(2)\r<BR>\n" );
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document.write( "use your calculator to get log(2^5) and use your calculator to get 5 * log(2)\r<BR>\n" );
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document.write( "both answers should be the same, namely 1.505149978\r<BR>\n" );
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document.write( " </SPAN>\n" );
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