document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=21493>Question 21493</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me solve this....<BR>\n" );
document.write( " In September 1998 the population of the country of West Goma in millions was modeled by f(x)=17.5e^0.0006x. At the same time the population of East Goma in millions was modeled by g(x)=14.1e^0.0187x. In both formulas x is the year, where x=0 corresponds to September 1998. Assuming these trends continue, estimate the year when the population of West Goma will equal the population of East Goma. <BR>\n" );
document.write( "The answer is 2010 but i have tried every method possible to come up with this answer please help...... </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #10377 by </B><A HREF=/tutors/aboutme.mpl?userid=mmm4444bot><B>mmm4444bot(95)</B></A><img src=\"/images/stars/stars-08.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=mmm4444bot><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=10377\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Hello There:\r<BR>\n" );
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document.write( "To solve this problem algebraically, we need to know a property of logarithms.\r<BR>\n" );
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document.write( "ln(a*b) = ln(a) + ln(b)\r<BR>\n" );
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document.write( "In other words, if we take the natural log of a product, that is the same as adding the natural logs of the factors.\r<BR>\n" );
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document.write( "We need to find the value of x such that f(x) = g(x).\r<BR>\n" );
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document.write( "17.5*e^(0.0006*x) = 14.1*e^(0.0187*x)\r<BR>\n" );
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document.write( "Take the natural log of both sides.\r<BR>\n" );
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document.write( "ln[17.5*e^(0.0006*x)] = ln[14.1*e^(0.0187*x)]\r<BR>\n" );
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document.write( "Now use the property described above to write each side as a sum of natural logs.\r<BR>\n" );
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document.write( "Remember that ln(e^x) = x, so ln[e^(0.0006*x)] = 0.0006*x.\r<BR>\n" );
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document.write( "ln(17.5) + 0.0006*x = ln(14.1) + 0.0187*x\r<BR>\n" );
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document.write( "Group like terms; subtract 0.0006*x and ln(14.1) from both sides.\r<BR>\n" );
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document.write( "0.0181*x = ln(17.5) - ln(14.1)\r<BR>\n" );
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document.write( "Use a calculator to evaluate the expression on the right side.\r<BR>\n" );
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document.write( "0.0181*x = 0.2160\r<BR>\n" );
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document.write( "Solve for x.\r<BR>\n" );
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document.write( "x = 11.9\r<BR>\n" );
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document.write( "Adding 12 years to 1998 gives the desired result.\r<BR>\n" );
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document.write( "~ Mark<BR>\n" );
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