document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1161308>Question 1161308</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Suppose that the population in a small city is 39,000 in the beginning of 2012 and the city council assumes that the population size t years later can be estimated by the equation\r<BR>\n" );
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document.write( "P=39,000e^0.09t\r<BR>\n" );
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document.write( "Approximately when will the city have a population of 60,000? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #784826 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=784826\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the equation is p = 39,000 * e^(.09*t)<BR>\n" );
document.write( "when the population is 60,000, the equation becomes:<BR>\n" );
document.write( "60,000 = 39,000 * e^(.09*t)<BR>\n" );
document.write( "divide both sides of the equation by 39,000 and simplify to get:<BR>\n" );
document.write( "60/39 = e^(.09*t)<BR>\n" );
document.write( "take the natural log of both sides of the equation to get:<BR>\n" );
document.write( "ln(60/39) = ln(e^(.09*t))<BR>\n" );
document.write( "by the properties of logarithms, this is equivalent to:<BR>\n" );
document.write( "ln(60/39) = .09*t*ln(e)<BR>\n" );
document.write( "since ln(e) = 1, this becomes:<BR>\n" );
document.write( "ln(60/39) = .09*t<BR>\n" );
document.write( "divide both sides of this equation by .09 and solve for t to get:<BR>\n" );
document.write( "t = ln(60/39)/.09 = 4.786476845<BR>\n" );
document.write( "confirm by replacing t in the original equation to get:<BR>\n" );
document.write( "f = 39,000 * e^(.09*4.786476845) = 60,000<BR>\n" );
document.write( "this confirms the solution is correct.<BR>\n" );
document.write( "since 39,000 population is in the beginning of 2012, and the population reaches 60,000 4.786476845 years from then, the population reaches 60,000 sometime in the year 2016.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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