document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=266547>Question 266547</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The population of a particular city is increasing at a rate proportional to its size. It follows the function P(t) = 1 + ke0.12t where k is a constant and t is the time in years. If the current population is 15,000, in how many years is the population expected to be 37,500? Round to the nearest year<BR>\n" );
document.write( "51<BR>\n" );
document.write( "8<BR>\n" );
document.write( "5<BR>\n" );
document.write( "3<BR>\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 #195831 by </B><A HREF=/tutors/aboutme.mpl?userid=drk><B>drk(1908)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=drk><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=195831\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> By saying current population, we create the coordinate: (0, 15000). We put that into<BR>\n" );
document.write( "(i) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28t%29+=+1+%2B+ke%5E%280.12t%29 ALIGN=MIDDLE  ALT=\"P%28t%29+=+1+%2B+ke%5E%280.12t%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "to get<BR>\n" );
document.write( "(ii) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15000+=+1+%2B+ke%5E%280.12%2A0%29 ALIGN=MIDDLE  ALT=\"15000+=+1+%2B+ke%5E%280.12%2A0%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "which is simply<BR>\n" );
document.write( "(iii) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1500+=+1+%2B+k ALIGN=MIDDLE  ALT=\"1500+=+1+%2B+k\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "so k = 14999<BR>\n" );
document.write( "Now, we rewrite the equation with our new k to get<BR>\n" );
document.write( "(iv) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28t%29+=+1+%2B+14999e%5E%280.12%2At%29 ALIGN=MIDDLE  ALT=\"P%28t%29+=+1+%2B+14999e%5E%280.12%2At%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "We are given 37000 as our new population number, place that into the equation and solve for t. we get<BR>\n" );
document.write( "(v) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=37000+=+1+%2B+14999e%5E%280.12%2At%29 ALIGN=MIDDLE  ALT=\"37000+=+1+%2B+14999e%5E%280.12%2At%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "subtract 1 and then divide by 14999 to get<BR>\n" );
document.write( "(vi) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2.46676+=+e%5E%280.12%2At%29 ALIGN=MIDDLE  ALT=\"2.46676+=+e%5E%280.12%2At%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "take an \"LN\" of both sides to get<BR>\n" );
document.write( "(vii) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=.902907+=+%280.12%2At%29 ALIGN=MIDDLE  ALT=\".902907+=+%280.12%2At%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "divide to get<BR>\n" );
document.write( "(viii) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+7.524 ALIGN=MIDDLE  ALT=\"t+=+7.524\"   DISABLED_style= \"max-width:90%; height:auto;\" > years<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "to the nearest year, it is 8. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );