document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=50196>Question 50196</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I don't have alot but I always have trouble when it comes to word problems.  Can you tell me if I have started correctly and if I have where I go from here.  Thanks!!  Andrea\r<BR>\n" );
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document.write( "The population of Cedar Rapids is expanding at a rate of P = P(sub0)e^kt,<BR>\n" );
document.write( "where P(sub0) is the current population, k is the expansion rate and t is time (in years). If the populations were 10,000 in 1990 and 12,000 in 2000, when will it reach 20,000?\r<BR>\n" );
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document.write( "I have t= 2006 with P(sub0)=unknown<BR>\n" );
document.write( "2000 is t-6=12,000<BR>\n" );
document.write( "1990 is t-16=10,000.\r<BR>\n" );
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document.write( "Not sure where to go now.\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #33342 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=33342\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The population of Cedar Rapids is expanding at a rate of P = P(sub0)e^kt,<BR>\n" );
document.write( "where P(sub0) is the current population, k is the expansion rate and t is time (in years). If the populations were 10,000 in 1990 and 12,000 in 2000, when will it reach 20,000? <BR>\n" );
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document.write( "P(t)=P(0)e^kt<BR>\n" );
document.write( "In ten years the population increased from 10000 to 12000, so:<BR>\n" );
document.write( "12000=10000e^k(10)<BR>\n" );
document.write( "1.2=e^(10k)<BR>\n" );
document.write( "Take the natural log of both sides to get:<BR>\n" );
document.write( "10k = ln1.2<BR>\n" );
document.write( "10k= 0.18<BR>\n" );
document.write( "k=0.018<BR>\n" );
document.write( "-------------<BR>\n" );
document.write( "Now you can rewrite the general equation as follows:<BR>\n" );
document.write( "P(t)=P(0)e^(0.018t)<BR>\n" );
document.write( "20000=10000e^(0.018t)<BR>\n" );
document.write( "2=e^0.018t<BR>\n" );
document.write( "ln2=0.018t<BR>\n" );
document.write( "t=0.693147.../0.018<BR>\n" );
document.write( "t=38.5 years\r<BR>\n" );
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document.write( "The 10000 corresponds to the year 1990<BR>\n" );
document.write( "38.5 years later will be 2029 when the population will be 20000<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
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