document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1129809>Question 1129809</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The population of Collin county, which follows the exponential growth model, increased from 491,272 in 2000 to 782,341 in 2010.\r<BR>\n" );
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document.write( "a. find the exponential growth rate, k. (let t=0 for year 2000) round to nearest four decimal. \r<BR>\n" );
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document.write( "b. white the exponential growth function.\r<BR>\n" );
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document.write( "c. what should the population have been in 2012?\r<BR>\n" );
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document.write( "d. when should the population be 1,245,863?\r<BR>\n" );
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document.write( "e. how long did it take population to double from what it was in 2000?\r<BR>\n" );
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document.write( "f. in 2017 population was 969,603. how does this compare with our model in part b? given this result what can you say about the growth of Collin county now? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #746614 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=746614\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> p=ak^t<BR>\n" );
document.write( "p1=491272*k^0<BR>\n" );
document.write( "p2=782341*k^10<BR>\n" );
document.write( "782341/491272 = k^10<BR>\n" );
document.write( "k=1.047629<BR>\n" );
document.write( "growth rate is 4.7629%\r<BR>\n" );
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document.write( "2012: predicted population is 491272*1.047629^12=858,642 people\r<BR>\n" );
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document.write( "1245863=491272*1.047629^t<BR>\n" );
document.write( "1.047629^k=2.5363599<BR>\n" );
document.write( "ln both sides is k ln 1.0476=ln 2.5363<BR>\n" );
document.write( "t=20.000 years.\r<BR>\n" );
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document.write( "Rule of 72 would say 72/4.76 or 15.12 years for doubling<BR>\n" );
document.write( "14.90 years \r<BR>\n" );
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document.write( "2017 predicted is 491272*1.0476^17 or 1083552, or more than actual, so the rate of growth is slowing down.<BR>\n" );
document.write( " </SPAN>\n" );
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