document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=159131>Question 159131</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Suppose that the number of new homes built, H, in a city over a period of time, t, is graphed on a rectangular coordinate system where time is on the horizontal axis. Suppose that the number of homes built can be modeled by an exponential function, H= p * at , where p is the number of new homes built in the first year recorded. If you were a homebuilder looking for work, would you prefer that the value of a to be between 0 and 1 or larger than 1? \r<BR>\n" );
document.write( "\n" );
document.write( "Assistance is requested with the equation ... below is what has been done.<BR>\n" );
document.write( "     When p > 0, a > 1, t gets larger, as well as y. When 0 < a < 1, then y gets continually smaller. As a homebuilder seeking work, the preference would be to have the value of a to larger than 1 (a > 1) to ensure plenty of work.<BR>\n" );
document.write( "H=500  t = 1   p = 5<BR>\n" );
document.write( "f(x)/t = p*ln(a)*a^t         <BR>\n" );
document.write( "y/1 = 5 (1) * 1^1<BR>\n" );
document.write( "1^1 = 2.72^1 (1)            <BR>\n" );
document.write( "(1) (2.72^1)/ 1    <BR>\n" );
document.write( "(1) 2.72* 1<BR>\n" );
document.write( "y = 2.72\r<BR>\n" );
document.write( "\n" );
document.write( "Thank you for the assistance.\r<BR>\n" );
document.write( "<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 #117325 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=117325\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Assistance is requested with the equation ... below is what has been done.<BR>\n" );
document.write( "When p > 0, a > 1, t gets larger, as well as y. When 0 < a < 1, then y gets continually smaller. As a homebuilder seeking work, the preference would be to have the value of a to larger than 1 (a > 1) to ensure plenty of work.<BR>\n" );
document.write( "--------------<BR>\n" );
document.write( "The equation is H = p*a^t<BR>\n" );
document.write( "----------------------------<BR>\n" );
document.write( "You are correct in saying that H is an increasing function when a>1 and<BR>\n" );
document.write( "a decreasing function when 0 < a < 1, like (1/2).<BR>\n" );
document.write( "----------------------<BR>\n" );
document.write( "I'm not sure what you are trying to do with the equation after that:<BR>\n" );
document.write( "H=500 t = 1 p = 5<BR>\n" );
document.write( "f(x)/t = p*ln(a)*a^t <BR>\n" );
document.write( "y/1 = 5 (1) * 1^1<BR>\n" );
document.write( "1^1 = 2.72^1 (1) <BR>\n" );
document.write( "(1) (2.72^1)/ 1 <BR>\n" );
document.write( "(1) 2.72* 1<BR>\n" );
document.write( "y = 2.72<BR>\n" );
document.write( "---------<BR>\n" );
document.write( "It appears you are letting t = 1 and p = 5 and H = 500<BR>\n" );
document.write( "If so you should get:<BR>\n" );
document.write( "500 = 5*a^1<BR>\n" );
document.write( "500 = 5a<BR>\n" );
document.write( "a = 100<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" );