document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1140196>Question 1140196</A>: <I><SPAN STYLE=\"word-break: break-all;\"> solve: suppose that 2000 is invested at interest rate k, compounded continuously, and grows to 2358.79 in 3 yrs. find the exponential growth function.<BR>\n" );
document.write( "find the doubling time<BR>\n" );
document.write( "please show work </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #760690 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=760690\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the continuous compounding formula is f = p * e^(r * n)\r<BR>\n" );
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document.write( "f is the future value<BR>\n" );
document.write( "p is the present value<BR>\n" );
document.write( "r is the interest rate per time period.<BR>\n" );
document.write( "n is the number of time periods.\r<BR>\n" );
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document.write( "when r = k, the formula becomes f = p * e ^ (k * n)\r<BR>\n" );
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document.write( "when f = 2358.79 and p = 2000 and n = 3 years, the formula becomes:\r<BR>\n" );
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document.write( "2358.79 = 2000 * e ^ (3 * k)\r<BR>\n" );
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document.write( "divide both sides of this equation by 2000 to get:\r<BR>\n" );
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document.write( "2358.79 / 2000 = e ^ (3 * k)\r<BR>\n" );
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document.write( "take the natural log of both sides of this equation to get:\r<BR>\n" );
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document.write( "ln(2358.79 / 2000) = ln(e ^ (3 * k))\r<BR>\n" );
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document.write( "since ln(e ^ (3 * k)) is equal to 3 * k * ln(e) and since ln(e) is equal to 1, the equation becomes:\r<BR>\n" );
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document.write( "ln(2358.79 / 2000) = 3 * k\r<BR>\n" );
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document.write( "divide both sides of this equation by 3 to get:\r<BR>\n" );
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document.write( "ln(2358.79 / 2000) / 3 = k\r<BR>\n" );
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document.write( "solve for k to get k = .0550005317\r<BR>\n" );
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document.write( "your exponential growth function is:\r<BR>\n" );
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document.write( "2358.79 = 2000 * e ^ (.0550005317 * 3).\r<BR>\n" );
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document.write( "evaluate this function to get 2358.79 = 2358.79, confirming the solution is correct.\r<BR>\n" );
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document.write( "to find the doubling time, the formula becomes:\r<BR>\n" );
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document.write( "2 = e ^ (.0550005317 * n)\r<BR>\n" );
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document.write( "take the natural log of both sides of this equation to get:\r<BR>\n" );
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document.write( "ln(2) = ln(e ^ (.0550005317 * n)\r<BR>\n" );
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document.write( "this becomes ln(2) = .0550005317 * n\r<BR>\n" );
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document.write( "divide both sides by .0550005317 to get:\r<BR>\n" );
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document.write( "ln(2) / .0550005317 = n\r<BR>\n" );
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document.write( "solve for n to get n = 12.602555418\r<BR>\n" );
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document.write( "replace n in the doubling formula to get:\r<BR>\n" );
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document.write( "2 = e ^ (.0550005317 * 12.602555418)\r<BR>\n" );
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document.write( "evaluate this function to get 2 = 2, confirming the solution is correct.\r<BR>\n" );
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document.write( "note that 2 = e ^ (.0550005317 * n) is the same as 2 = 1 * e ^ (.0550005317 * n)\r<BR>\n" );
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document.write( "you future value is 2 and your present value is 1, hence the doubling.<BR>\n" );
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