document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1157178>Question 1157178</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The population of a certain city was 110,000 in 2014, and the observed doubling time for the population is 18 years.<BR>\n" );
document.write( "(a) Find an exponential model <BR>\n" );
document.write( "n(t) = n02t/a<BR>\n" );
document.write( " for the population t years after 2014.<BR>\n" );
document.write( "n(t) = <BR>\n" );
document.write( " \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "(b) Find an exponential model <BR>\n" );
document.write( "n(t) = n0ert<BR>\n" );
document.write( " for the population t years after 2014. (Round your r value to four decimal places.)<BR>\n" );
document.write( "n(t) = <BR>\n" );
document.write( " \r<BR>\n" );
document.write( "\n" );
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 #780011 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=780011\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> exponential model is n(t) = ab^t<BR>\n" );
document.write( "a = 110<BR>\n" );
document.write( "n(t) = 220<BR>\n" );
document.write( "t = 18<BR>\n" );
document.write( "solve for b<BR>\n" );
document.write( "you get:<BR>\n" );
document.write( "220 = 110 * b^18<BR>\n" );
document.write( "divide both sides of this equation by 110 to get<BR>\n" );
document.write( "2 = b^18<BR>\n" );
document.write( "take the 18th root of both sides of the equation to get:<BR>\n" );
document.write( "2^(1/18) = b<BR>\n" );
document.write( "solve for b to get:<BR>\n" );
document.write( "b = 1.039259226...<BR>\n" );
document.write( "store that in your calculator and then confirm by replacing b with that to get:<BR>\n" );
document.write( "n(t) = 110 * (1.039259226...)^18 = 220.<BR>\n" );
document.write( "your equation is:<BR>\n" );
document.write( "n(t) = 110 * (1.039259226...)^t<BR>\n" );
document.write( "here's a graph of that equation after replacing n(t) with y and t with x.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2020/042602.jpg\" alt=\"$$$\" ><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );