document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1010384>Question 1010384</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 a decreasing population? By what percentage is the population of that country decreasing 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 #625828 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=625828\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the formula with the negative exponent is modelling a decrease.\r<BR>\n" );
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document.write( "that formula is the formula for russia, which is a = 142.9e^-.004t.\r<BR>\n" );
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document.write( "the general formula is a = p * e^rt\r<BR>\n" );
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document.write( "r is the growth rate per time period<BR>\n" );
document.write( "t is the number of time periods<BR>\n" );
document.write( "a is the future value<BR>\n" );
document.write( "p is the present value\r<BR>\n" );
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document.write( "t = 0 when the year is 2006.\r<BR>\n" );
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document.write( "in 2006, russia had 142.9 * e^(-.004*0) = 142.9 million people.\r<BR>\n" );
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document.write( "in 2007, russia has 142.9 * e^(-.004*1) = 142.3295417 million people.\r<BR>\n" );
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document.write( "to translate from continuous compounding to annual compounding, 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( "ar is the annual compounging rate.<BR>\n" );
document.write( "cr is the continuous compounding rate.\r<BR>\n" );
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document.write( "when cr = -.004, the formula becomes:\r<BR>\n" );
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document.write( "(1+ar) = e^-.004)\r<BR>\n" );
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document.write( "this results in (1+ar) = .9960079893\r<BR>\n" );
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document.write( "to solve for ar, subtract 1 form both sides of the equation to get:\r<BR>\n" );
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document.write( "ar = -.0039920107\r<BR>\n" );
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document.write( "the annual compounding rate is -.0039920107.\r<BR>\n" );
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document.write( "multiply this by 100 to get an annual compounding rate percent of -.39920107%.\r<BR>\n" );
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document.write( "this means the russian population is decreasing by .39920107% per year rounded to 8 decimal places.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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