document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1201103>Question 1201103</A>: <I><SPAN STYLE=\"word-break: break-all;\"> According to the U.S. Census Bureau, the population of the United States in 2008 was 304 million people. In addition, the population of the United States was growing at a rate of 1.1% per year. Assuming this growth rate is continues, the model\r<BR>\n" );
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document.write( "P(t)=304*(1.011)^t-2008\r<BR>\n" );
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document.write( "represents the population P (in millions of people) in year t.\r<BR>\n" );
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document.write( "According to the model, when will the population be 412 million people? Be sure to round your answer to the nearest whole year.\r<BR>\n" );
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document.write( "Year _____<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #835361 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=835361\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> population in 2008 = 304 million.<BR>\n" );
document.write( "formula is f = p * (1+r) ^ n<BR>\n" );
document.write( "when r = .011 (1.1%), the formula bcomes:<BR>\n" );
document.write( "f = 304 * 1.011 ^ n<BR>\n" );
document.write( "n is the number of years from 2008.<BR>\n" );
document.write( "when f = 412 million, the formula becomes:<BR>\n" );
document.write( "412 = 304 * 1.011 ^ n<BR>\n" );
document.write( "divide both sides of the equation by 304 to get:<BR>\n" );
document.write( "412/304 = 1.011 ^ n<BR>\n" );
document.write( "take the log of both sides of this equation to get:<BR>\n" );
document.write( "log(412/304) = log(1.011 ^ n)<BR>\n" );
document.write( "by log rule that says log(b^n) = n * log(b), this becomes:<BR>\n" );
document.write( "log(412/304) = n * log(1.011)<BR>\n" );
document.write( "solve for n to get:<BR>\n" );
document.write( "n = log(412/304) / log(1.011) = 27.78768868.<BR>\n" );
document.write( "replace n in the original equation with that and solve for f to get:<BR>\n" );
document.write( "f = 304 * 1.011 ^ 27.78768868 = 412.<BR>\n" );
document.write( "this confirms the value of n is correct.<BR>\n" );
document.write( "the population will grow to 412 million in 27.78768868 years after the end of 2008.<BR>\n" );
document.write( "that would make it at the end of 2008 + that = at the end of 2035.787689.<BR>\n" );
document.write( "that would be in the year 2036.<BR>\n" );
document.write( "at the end of 2035, the population will be 304 * 1.011 ^ (2035 - 2008) = 408.4649392.<BR>\n" );
document.write( "at the end of 2036, the population will be 304 * 1.011 ^ (2036 - 2008) = 412.9580535.<BR>\n" );
document.write( "it becomes 412 some time between the end of 2035 and the end of 2036.\r<BR>\n" );
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