document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1171138>Question 1171138</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 	 <BR>\n" );
document.write( "In​ 2012, the population of a city was 5.21 million. The exponential growth rate was ​2.86% per year.\r<BR>\n" );
document.write( "\n" );
document.write( "a) Find the exponential growth function.<BR>\n" );
document.write( "​b) Estimate the population of the city in 2018.<BR>\n" );
document.write( "​c) When will the population of the city be 9 ​million?<BR>\n" );
document.write( "​d) Find the doubling time. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #796037 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=796037\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> In​ 2012, the population of a city was 5.21 million. The exponential growth rate was ​2.86% per year.<BR>\n" );
document.write( "a) Find the exponential growth function.<BR>\n" );
document.write( "t - time in years, pop in millions<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28t%29+=+5.21%281.0286%29%5Et ALIGN=MIDDLE  ALT=\"f%28t%29+=+5.21%281.0286%29%5Et\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ":<BR>\n" );
document.write( "​b) Estimate the population of the city in 2018.<BR>\n" );
document.write( "t = 6 yrs<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28t%29+=+5.21%281.0286%29%5E6 ALIGN=MIDDLE  ALT=\"f%28t%29+=+5.21%281.0286%29%5E6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "f(t) =  5.21 * 1.1843<BR>\n" );
document.write( "f(t) = 6.17 million in 2018 (6 yrs)<BR>\n" );
document.write( ":<BR>\n" );
document.write( "​c) When will the population of the city be 9 ​million?<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5.21%281.0286%29%5Et+=+9 ALIGN=MIDDLE  ALT=\"5.21%281.0286%29%5Et+=+9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281.0286%29%5Et+=+9%2F5.21 ALIGN=MIDDLE  ALT=\"%281.0286%29%5Et+=+9%2F5.21\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281.0286%29%5Et+=+1.727 ALIGN=MIDDLE  ALT=\"%281.0286%29%5Et+=+1.727\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "use common logs here<BR>\n" );
document.write( "t*log(1.0286) = log(1.727)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+log%281.727%29%2Flog%281.086%29 ALIGN=MIDDLE  ALT=\"t+=+log%281.727%29%2Flog%281.086%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "use your calc<BR>\n" );
document.write( "t = 19.37 yrs<BR>\n" );
document.write( ":<BR>\n" );
document.write( "​d) Find the doubling time.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281.0286%29%5Et+=+2 ALIGN=MIDDLE  ALT=\"%281.0286%29%5Et+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "t = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%282%29%2Flog%281.086%29 ALIGN=MIDDLE  ALT=\"log%282%29%2Flog%281.086%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "t = 24.59 yrs to double </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );