document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=83895>Question 83895</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The population of the United States in 1994 was about 260 million, and the population was about 277 million in 2003.\r<BR>\n" );
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document.write( "Find the growth rate in the United States and write an exponential function describing this situation.\r<BR>\n" );
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document.write( "What was the projected percent of increase annually?\r<BR>\n" );
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document.write( "The population was/will be 1 billion in what year? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #60367 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=60367\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The population of the United States in 1994 was about 260 million, and the population was about 277 million in 2003.\r<BR>\n" );
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document.write( "Find the growth rate in the United States and write an exponential function describing this situation.<BR>\n" );
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document.write( "growth rate = [one year change in population]/260 = [277-260]/9/260 = 17/9/260=1.8888/260=0.007<BR>\n" );
document.write( "EQUATION:<BR>\n" );
document.write( "P(t) = 260(1.007)^t ( in millions)<BR>\n" );
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document.write( "What was the projected percent of increase annually?<BR>\n" );
document.write( "% increase = [one year increase/last year total] = 1.88888/260 = 0.007 or 0.7%<BR>\n" );
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document.write( "The population was/will be 1 billion in what year?\r<BR>\n" );
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document.write( "Comment: 1000 million = 1 billion<BR>\n" );
document.write( "Let P(t) = 1000; find \"t\":<BR>\n" );
document.write( "1000 = 260 (1.007)^t<BR>\n" );
document.write( "Divide both sides by 260 to get:<BR>\n" );
document.write( "3.84615.. = (1.007)^t<BR>\n" );
document.write( "Take the log of both sides:<BR>\n" );
document.write( "tlog(1.007) = log3.84615<BR>\n" );
document.write( "t = [log3.84615]/[log(1.007)]<BR>\n" );
document.write( "t = 193.11 years<BR>\n" );
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document.write( "1994 + 193 = 2187<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( " </SPAN>\n" );
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