document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=129419>Question 129419</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need help with this question\r<BR>\n" );
document.write( "\n" );
document.write( "A midwestern city finds its resident moving to the suburbs.  Its population is declining according to the function defined by P(t)=poe-0.04t, where t is time in years and P0 is the population at time t=0.  Assume that P0=1,000,000.\r<BR>\n" );
document.write( "\n" );
document.write( "I need to find the population at time t=1.\r<BR>\n" );
document.write( "\n" );
document.write( "b) how long will it take for the population to decline to 750,000?\r<BR>\n" );
document.write( "\n" );
document.write( "c) how long will it take for the population to decline to half the initial number? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #94535 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=94535\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28t%29=P%5B0%5De%5E%28-0.04t%29 ALIGN=MIDDLE  ALT=\"P%28t%29=P%5B0%5De%5E%28-0.04t%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28t%29=%281000000%29e%5E%28-0.04t%29 ALIGN=MIDDLE  ALT=\"P%28t%29=%281000000%29e%5E%28-0.04t%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "a) At time t=1,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%281%29=%281000000%29e%5E%28-0.04%281%29%29 ALIGN=MIDDLE  ALT=\"P%281%29=%281000000%29e%5E%28-0.04%281%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Substitute t=1.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%281%29=%281000000%29%280.960789%29 ALIGN=MIDDLE  ALT=\"P%281%29=%281000000%29%280.960789%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%281%29=960789 ALIGN=MIDDLE  ALT=\"P%281%29=960789\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "At 1 year, the population is now at 960,789.\r<BR>\n" );
document.write( "\n" );
document.write( "b)<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28t%29=%281000000%29e%5E%28-0.04t%29=750000 ALIGN=MIDDLE  ALT=\"P%28t%29=%281000000%29e%5E%28-0.04t%29=750000\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e%5E%28-0.04t%29=0.75 ALIGN=MIDDLE  ALT=\"e%5E%28-0.04t%29=0.75\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-0.04t=ln%280.75%29 ALIGN=MIDDLE  ALT=\"-0.04t=ln%280.75%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Take the natural log of both sides.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-0.04t=-0.28768 ALIGN=MIDDLE  ALT=\"-0.04t=-0.28768\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=7.19 ALIGN=MIDDLE  ALT=\"t=7.19\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The time to reach 750,000 people would be 7.19 years (approximately 7 years, 2 months).<BR>\n" );
document.write( "c)<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28t%29=%281000000%29e%5E%28-0.04t%29=500000 ALIGN=MIDDLE  ALT=\"P%28t%29=%281000000%29e%5E%28-0.04t%29=500000\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-0.04t=ln%280.50%29 ALIGN=MIDDLE  ALT=\"-0.04t=ln%280.50%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Take the natural log of both sides. <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-0.04t=-0.69315 ALIGN=MIDDLE  ALT=\"-0.04t=-0.69315\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=17.33 ALIGN=MIDDLE  ALT=\"t=17.33\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The time to reach 500,000 people would be 17.33 years (approximately 17 years, 4 months). </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );