document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=867252>Question 867252</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The population of a town in the year 2000 was 250million and the population growth rate is 0.55% per year. Use the population model P(t)=P0(1+r)^t to find the year when the population reaches 350million. Answer is 2061\r<BR>\n" );
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document.write( "I can't figure out what numbers to plug into what function to solve this. The only example I have of using this formula isn't finding a year so it's not working. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #522971 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=522971\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Formulas and recipes are overrated.<BR>\n" );
document.write( "0.55% =<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.55%2F100=0.0055 ALIGN=MIDDLE  ALT=\"0.55%2F100=0.0055\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The increase in population after the first year is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.0055%2AP%5B0%5D ALIGN=MIDDLE  ALT=\"0.0055%2AP%5B0%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "So the population goes from <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%5B0%5D ALIGN=MIDDLE  ALT=\"P%5B0%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > to<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%5B0%5D%2B0.0055%2AP%5B0%5D=1.0055%2AP%5B0%5D ALIGN=MIDDLE  ALT=\"P%5B0%5D%2B0.0055%2AP%5B0%5D=1.0055%2AP%5B0%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "The population increases by the same <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.0055 ALIGN=MIDDLE  ALT=\"1.0055\"   DISABLED_style= \"max-width:90%; height:auto;\" > factor every year.<BR>\n" );
document.write( "After <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t ALIGN=MIDDLE  ALT=\"t\"   DISABLED_style= \"max-width:90%; height:auto;\" > years, the population is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28t%29=P%5B0%5D%2A1.0055%5Et ALIGN=MIDDLE  ALT=\"P%28t%29=P%5B0%5D%2A1.0055%5Et\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "You need to find the time <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t ALIGN=MIDDLE  ALT=\"t\"   DISABLED_style= \"max-width:90%; height:auto;\" > years after 2000, when <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28t%29=350million ALIGN=MIDDLE  ALT=\"P%28t%29=350million\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "knowing that in 2000, the population is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%5B0%5D=250million ALIGN=MIDDLE  ALT=\"P%5B0%5D=250million\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=350million=250million%2A1.0055%5Et ALIGN=MIDDLE  ALT=\"350million=250million%2A1.0055%5Et\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=350million%2F%22250+million%22+=1.0055%5Et ALIGN=MIDDLE  ALT=\"350million%2F%22250+million%22+=1.0055%5Et\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%2F5+=1.0055%5Et ALIGN=MIDDLE  ALT=\"7%2F5+=1.0055%5Et\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.4=1.0055%5Et ALIGN=MIDDLE  ALT=\"1.4=1.0055%5Et\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Taking logarithms on both sides of the equal sign<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%281.4%29=log%281.0055%5Et%29 ALIGN=MIDDLE  ALT=\"log%281.4%29=log%281.0055%5Et%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%281.4%29=t%2Alog%281.0055%29 ALIGN=MIDDLE  ALT=\"log%281.4%29=t%2Alog%281.0055%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=log%281.4%29%2Flog%281.0055%29 ALIGN=MIDDLE  ALT=\"t=log%281.4%29%2Flog%281.0055%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "That yields <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=61 ALIGN=MIDDLE  ALT=\"t=61\"   DISABLED_style= \"max-width:90%; height:auto;\" > (rounded to nthe nearest integer.<BR>\n" );
document.write( "So the population reaches 350million 61 years after 2000,<BR>\n" );
document.write( "in the year 2061.<BR>\n" );
document.write( " <BR>\n" );
document.write( "NOTE:<BR>\n" );
document.write( "Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.0055=e%5Eln%281.0055%29 ALIGN=MIDDLE  ALT=\"1.0055=e%5Eln%281.0055%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.0055%5Et=%28e%5Eln%281.0055%29%29%5Et=e%5E%28t%2Aln%281.0055%29%29 ALIGN=MIDDLE  ALT=\"1.0055%5Et=%28e%5Eln%281.0055%29%29%5Et=e%5E%28t%2Aln%281.0055%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "and math teachers really like the irrational number <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e ALIGN=MIDDLE  ALT=\"e\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "they often write the function as<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28t%29=P%5B0%5D%2Ae%5E%28t%2Aln%281.0055%29%29 ALIGN=MIDDLE  ALT=\"P%28t%29=P%5B0%5D%2Ae%5E%28t%2Aln%281.0055%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "It is really the same thing. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );