document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=425275>Question 425275</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hello, I need help with an exponential growth model word problem :<BR>\n" );
document.write( "The population of Houston Texas was 2.30 million in 1990, and 2.65 million in 2000. Using an exponential growth model, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+ne%5Ekt+ ALIGN=MIDDLE  ALT=\"+y+=+ne%5Ekt+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, sketch a graph of the population beginning in 1990 and find the predicted population in 2010\r<BR>\n" );
document.write( "\n" );
document.write( "I checked my exponential growth notes but the formula was not the same it is: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+a+sqrt%28+x-h+%29+%2B+k+ ALIGN=MIDDLE  ALT=\"+y+=+a+sqrt%28+x-h+%29+%2B+k+\"   DISABLED_style= \"max-width:90%; height:auto;\" > and we found the vertex from that (which is the \"h\" and \"k\"), then made our graphs. I checked online and there was a calculater for it and that gave me an answer of 76.16554 which I do not think has anything to do with this question.  Thank you so much for your time. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #296169 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=296169\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The population of Houston Texas was 2.30 million in 1990, <BR>\n" );
document.write( "and 2.65 million in 2000. Using an exponential growth model,  y = ne^kt , sketch a graph of the population beginning in 1990 and find the predicted population in 2010<BR>\n" );
document.write( "----<BR>\n" );
document.write( "In 2000 t is 10<BR>\n" );
document.write( "2.65 = n*e^10k<BR>\n" );
document.write( "In 1990 t is zero.<BR>\n" );
document.write( "2.30 = n*e^0<BR>\n" );
document.write( "---<BR>\n" );
document.write( "So n = 2.30<BR>\n" );
document.write( "---<BR>\n" );
document.write( "So 2.65 = 2.30*e^10k<BR>\n" );
document.write( "---<BR>\n" );
document.write( "So e^10k = 1.152174<BR>\n" );
document.write( "Take the natural log of both sides to get:<BR>\n" );
document.write( "10k = 0.141651<BR>\n" );
document.write( "k = 0.014165<BR>\n" );
document.write( "---<BR>\n" );
document.write( "Equation:<BR>\n" );
document.write( "y = 2.30*e^(0.014165t)<BR>\n" );
document.write( "find the predicted population in 2010<BR>\n" );
document.write( "In 2010 t = 20<BR>\n" );
document.write( "y = 2.30*e^(0.014165*20)<BR>\n" );
document.write( "y = 3.053258 million<BR>\n" );
document.write( "=========================<BR>\n" );
document.write( "Graph:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C300%2C-5%2C25%2C-5%2C5%2C2.30%2A%282.718281828%29%5E%280.014165x%29%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C300%2C-5%2C25%2C-5%2C5%2C2.30%2A%282.718281828%29%5E%280.014165x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "=========================<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( "============= </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );