document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1010383>Question 1010383</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Directions: The exponential models describe the population of the indicated country, A, in millions, t years after 2006. Use these models to solve.  India A=1095.4e^0.014t Iraq A=26.8e^0.027t Japan A= 127.5e^0.001t Russia A=142.9e^-0.004t <BR>\n" );
document.write( "Which country has the greatest growth rate? By what percentage is the population of that country increasing each year?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #625829 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=625829\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the general formula for continuous compounding is:\r<BR>\n" );
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document.write( "A = p * e^(rt)\r<BR>\n" );
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document.write( "A is the future value<BR>\n" );
document.write( "p is the present value<BR>\n" );
document.write( "r is the continuous compounding growth rate per time period.<BR>\n" );
document.write( "t is the numbe of time periods.\r<BR>\n" );
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document.write( "the time periods for this problem are expressed in years.\r<BR>\n" );
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document.write( "the country with the highest value of r has the highest continuous compounding growth rate.\r<BR>\n" );
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document.write( "that country would be iraq with a continuous compounding growth rate of .027 per year.\r<BR>\n" );
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document.write( "to convert from continuous compounding growth rate to annual compounding growth rate, use the following formula.\r<BR>\n" );
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document.write( "(1+ar) = e^cr\r<BR>\n" );
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document.write( "when cr = .027, that formula becomes:\r<BR>\n" );
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document.write( "(1+ar) = e^.027 = 1.027367803\r<BR>\n" );
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document.write( "to solve for ar, subtract 1 from both sides of the equation to get:\r<BR>\n" );
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document.write( "ar = .027367803.\r<BR>\n" );
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document.write( "that's the annual compounding growth rate.\r<BR>\n" );
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document.write( "the annual compounding growth rate percent is equal to 2.7367803%.\r<BR>\n" );
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document.write( "the population in iraq is growing at a rate of 2.7367803% per year.\r<BR>\n" );
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document.write( "since the formulas are equivalent, they should yield the same result.\r<BR>\n" );
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document.write( "using continuous compounding formula for 1 year:\r<BR>\n" );
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document.write( "26.8 * e^.027 = 27.53345711\r<BR>\n" );
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document.write( "using annual compounding formula for 1 year:\r<BR>\n" );
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document.write( "26.8 * (1.027367803) = 27.53345711\r<BR>\n" );
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document.write( "they're the same, confirming that the two formulas are equivalent.\r<BR>\n" );
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document.write( "the annual growth rate for all of the countries is shown below:\r<BR>\n" );
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document.write( "india:<BR>\n" );
document.write( "e^.014 = 1.014098459 - 1 = .014098459 = 1.4098459%<BR>\n" );
document.write( "iraq:<BR>\n" );
document.write( "e^.027 = 1.027367803 - 1 = .027367803 = 2.7367805%<BR>\n" );
document.write( "japan:<BR>\n" );
document.write( "e^.001 = 1.0010005 - 1 = .0010005 = 1.0005%<BR>\n" );
document.write( "russia:<BR>\n" );
document.write( "e^-.004 = .9960079893 - 1 = -.0039920107 = -.39920107%\r<BR>\n" );
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document.write( " </SPAN>\n" );
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