document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1075515>Question 1075515</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The population of Dallas County, which follows the exponential growth model, increaed from 491,675 in 2000 to 782,341 in 2010. <BR>\n" );
document.write( "A- Find the exponential growth rate, k. <BR>\n" );
document.write( "B- Write the exponential growth funtion. Use growth rate found in a.<BR>\n" );
document.write( "C- What should the population be in 2016? Use function from b.<BR>\n" );
document.write( "D- When should the population be 999,999? use the funtion from b.<BR>\n" );
document.write( "E- How long will it take the population to double? Use growth rate found in A. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #690164 by </B><A HREF=/tutors/aboutme.mpl?userid=jorel1380><B>jorel1380(3719)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jorel1380><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=jorel1380><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=690164\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A. 782341/491675=1.5911750648294096710225250419484, or a growth rate of 59% over 10 years. So:<BR>\n" );
document.write( "(1+k)^10=1.5911750648294096710225250419484<BR>\n" );
document.write( "ln (1+k)^10= ln 1.5911750648294096710225250419484<BR>\n" );
document.write( "10 ln(1+k)=ln 1.5911750648294096710225250419484<BR>\n" );
document.write( "ln(1+k)=ln 1.5911750648294096710225250419484/10=0.04644727777645335179835425806392<BR>\n" );
document.write( "e^0.04644727777645335179835425806392=1+k<BR>\n" );
document.write( "k=1.0475428488243655419718940009655, or 4.75428488243655419718940009655% growth rate per year.<BR>\n" );
document.write( "B. Population year t=491675 x (1.0475)^(t-2000)<BR>\n" );
document.write( "C. Population in 2016=491675 x (1.0475)^16=1033100.64 people<BR>\n" );
document.write( "D. 999999=491675 x (1.0475)^(t-2000)<BR>\n" );
document.write( "2.0338617989525601260995576346164=(1.0475)^(t-2000)<BR>\n" );
document.write( "By the previous process we get t=15.298251227477130099351978599649, or the desired population of 999999 somewhere soon after January, 2015.<BR>\n" );
document.write( "E.For the initial population to double, we have:<BR>\n" );
document.write( "2=1.0475^t<BR>\n" );
document.write( "ln 2=ln 1.0475^t<BR>\n" );
document.write( "ln 2=t ln 1.0475<BR>\n" );
document.write( "t=approximate 15.3 years for the population to double at the current rate. &#9786;&#9786;&#9786;&#9786; </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );