document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=102455>Question 102455</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The future population of a town t years after January 1, 1995 is described in thousands by function P(t) = 120 + 4t + 0.05t2. Calculate the value of P(5) and explain it means. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #74534 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=74534\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Given:<BR>\n" );
document.write( ". <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28t%29+=+120+%2B+4t+%2B+0.05t%5E2 ALIGN=MIDDLE  ALT=\"P%28t%29+=+120+%2B+4t+%2B+0.05t%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "This function models the population (in thousands) of a town starting on January 1, 1995. <BR>\n" );
document.write( ".<BR>\n" );
document.write( "The clock starts running on January 1, 1995. On that date t is equal to zero. So if you go<BR>\n" );
document.write( "to the given function and substitute zero for t, you get the population of the town on that <BR>\n" );
document.write( "date. Let's do it ...<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%280%29+=+120+%2B+4%2A%280%29+%2B+0.05%2A%280%29%5E2+=+120+%2B+0+%2B+0+=+120 ALIGN=MIDDLE  ALT=\"P%280%29+=+120+%2B+4%2A%280%29+%2B+0.05%2A%280%29%5E2+=+120+%2B+0+%2B+0+=+120\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "So on January 1, 1995 the population of the town is 120 thousand or 120,000.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Five years later [you get that from P(5)] is January 1, 2000. We can find the population of <BR>\n" );
document.write( "the town on that date by substituting 5 into the given equation in place of t. When we do, the<BR>\n" );
document.write( "equation becomes:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%285%29+=+120+%2B+4%2A%285%29+%2B+0.05%2A%285%5E2%29+=+120+%2B+20+%2B+0.05%2A25+=+120+%2B+20+%2B+1.25 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Adding up the three terms tells us that on January 1, 2000 the population of the town is:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=120+%2B+20+%2B+1.25+=+141.25+ ALIGN=MIDDLE  ALT=\"120+%2B+20+%2B+1.25+=+141.25+\"   DISABLED_style= \"max-width:90%; height:auto;\" > thousand or 141,250.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "This means that in the first five years, the town's population grows from 120,000 to<BR>\n" );
document.write( "141,250 ... a gain of 21,250.  <BR>\n" );
document.write( ".<BR>\n" );
document.write( "Hope this helps you to see your way through this problem.  <BR>\n" );
document.write( ".<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );