document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=697075>Question 697075</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The population of a town was 10 million on January 1, 2009.  The exponential growth function <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=Pe%5E0.04t ALIGN=MIDDLE  ALT=\"A=Pe%5E0.04t\"   DISABLED_style= \"max-width:90%; height:auto;\" > represents the population of the town.  If A represents the population of this town t, years after 2009 and P is the original population.  In what year will the population first surpass 15 million?\r<BR>\n" );
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document.write( "My teacher has us first figure out what each letter stands for:\r<BR>\n" );
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document.write( "15 million A:population of the town<BR>\n" );
document.write( "X t: time (years)<BR>\n" );
document.write( "10 million p: original population\r<BR>\n" );
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document.write( "I'm not sure where the numbers go. meaning, does A=15 million, t is what we are solving for, and P is 10 million? They give 10 million as the towns population and ask what year it will surpass to 15 million. would this be the equation:\r<BR>\n" );
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document.write( "15,000,000=10,000,000<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e%5E0.04t ALIGN=MIDDLE  ALT=\"e%5E0.04t\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "if so this is how to solve the word problem, this is how I continued to solve it:\r<BR>\n" );
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document.write( "15,000,000=10,000,000<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e%5E0.04t ALIGN=MIDDLE  ALT=\"e%5E0.04t\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "5,000,000=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e%5E0.04t ALIGN=MIDDLE  ALT=\"e%5E0.04t\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "then I used Ln and got 5,000,000=0.04t. Then I divided out 0.04 and got 125,000,000. \r<BR>\n" );
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document.write( "I know this is wrong. I'm pretty sure it is going to be a logarithm question, I'm just not sure how to set up the exponential growth equation with the given numbers.\r<BR>\n" );
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document.write( "Thank you for your help and for your time.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #429639 by </B><A HREF=/tutors/aboutme.mpl?userid=nerdybill><B>nerdybill(7384)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=nerdybill><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=nerdybill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=429639\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Your equation below is correct:<BR>\n" );
document.write( "15,000,000=10,000,000<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e%5E%280.04t%29 ALIGN=MIDDLE  ALT=\"e%5E%280.04t%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "dividing each side by 100000:<BR>\n" );
document.write( "15=10<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e%5E%280.04t%29 ALIGN=MIDDLE  ALT=\"e%5E%280.04t%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "15/10 = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e%5E%280.04t%29 ALIGN=MIDDLE  ALT=\"e%5E%280.04t%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "3/2 = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e%5E%280.04t%29 ALIGN=MIDDLE  ALT=\"e%5E%280.04t%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "now, you take the \"natural log\" (ln) of both sides to get:<BR>\n" );
document.write( "ln(3/2) = 0.04t<BR>\n" );
document.write( "ln(3/2)/0.04 = t<BR>\n" );
document.write( "10.14 = t<BR>\n" );
document.write( "that's 10.14 years after January 1, 2009:<BR>\n" );
document.write( "so, that's approximately:<BR>\n" );
document.write( "March 1, 2019 </SPAN>\n" );
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