document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1186442>Question 1186442</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Assume the number of U.S. dial-up Internet households stood at 42.5 million at the beginning of 2004 and was projected to decline at the rate of 3.9 million households per year for the next 7 years.<BR>\n" );
document.write( "(a) Find a linear function f giving the projected U.S. dial-up Internet households (in millions) in year t, where t = 0 corresponds to the beginning of 2004.<BR>\n" );
document.write( "(b) What is the projected number of U.S. dial-up Internet households at the beginning of 2011?<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 #849441 by </B><A HREF=/tutors/aboutme.mpl?userid=CPhill><B>CPhill(1959)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=CPhill><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=CPhill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=849441\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> **(a) Finding the linear function:**\r<BR>\n" );
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document.write( "Since the number of households is declining at a constant rate, we can model this situation with a linear function of the form:\r<BR>\n" );
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document.write( "f(t) = mt + b\r<BR>\n" );
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document.write( "where:\r<BR>\n" );
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document.write( "* f(t) is the projected number of households (in millions) in year t<BR>\n" );
document.write( "* m is the slope (rate of change)<BR>\n" );
document.write( "* b is the y-intercept (initial number of households)\r<BR>\n" );
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document.write( "We are given:\r<BR>\n" );
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document.write( "* b = 42.5 million (initial number of households at t = 0)<BR>\n" );
document.write( "* m = -3.9 million households per year (decline rate, so it's negative)\r<BR>\n" );
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document.write( "Therefore, the linear function is:\r<BR>\n" );
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document.write( "f(t) = -3.9t + 42.5\r<BR>\n" );
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document.write( "**(b) Projecting households at the beginning of 2011:**\r<BR>\n" );
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document.write( "Since t = 0 corresponds to the beginning of 2004, the beginning of 2011 corresponds to t = 2011 - 2004 = 7.\r<BR>\n" );
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document.write( "We can now plug t = 7 into our linear function:\r<BR>\n" );
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document.write( "f(7) = -3.9 * 7 + 42.5<BR>\n" );
document.write( "f(7) = -27.3 + 42.5<BR>\n" );
document.write( "f(7) = 15.2\r<BR>\n" );
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document.write( "So, the projected number of U.S. dial-up Internet households at the beginning of 2011 is 15.2 million.<BR>\n" );
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