document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=554457>Question 554457</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Use of the Internet in a country is given by the function f(x)=0.485x^2-1.694x+0.315, where the output is in millions of users.  In this formula z=6 corresponds to 1996-x=20 which corresponds to 2010.  Estimate when the number of Internet uses in the country reached 150 million.\r<BR>\n" );
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document.write( "Since the function contains decimal coefficients, we have decided to solve this problem by graphing.  To determine when the number of uses reach 150 million, find the x-value of the point where the functions g(x)-18 and f(x)-0.485x^2-1.694x+0.315 intersect. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #361365 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=361365\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> f(x) = .485x^2 - 1.694x + .315.<BR>\n" );
document.write( "output is in millions of users.<BR>\n" );
document.write( "i don't understand what you mean by when z = 6 and g(18).<BR>\n" );
document.write( "i graphed the function to see what was happening.<BR>\n" );
document.write( "here's what the graph looks like.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28600%2C600%2C-5%2C35%2C-20%2C200%2C.485x%5E2-1.694x%2B.315%2C150%29 ALIGN=MIDDLE  ALT=\"graph%28600%2C600%2C-5%2C35%2C-20%2C200%2C.485x%5E2-1.694x%2B.315%2C150%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "did you mean when z = 6 corresponds to 1996 - 6 + 20 = 2010?<BR>\n" );
document.write( "did you mean x?<BR>\n" );
document.write( "i think you must have.<BR>\n" );
document.write( "you could have simplified it by saying that the year is 2004 when x = 0<BR>\n" );
document.write( "then, when x = 6, the year would be 2004 + 6 = 2010.<BR>\n" );
document.write( "at least i think that's what you meant.<BR>\n" );
document.write( "if the output is in millions of user, then the y = 150 would equate to 150 million users.<BR>\n" );
document.write( "you would need to find the value of x for when y = 150.<BR>\n" );
document.write( "per the graph, this would occur somewhere around the point where x = 19.<BR>\n" );
document.write( "that looks to be somewhere around when x = 18 that you mentioned.<BR>\n" );
document.write( "that would not be g(x) = 18.<BR>\n" );
document.write( "that would be x = 18<BR>\n" );
document.write( "when x = 18, the value of y = 126.963<BR>\n" );
document.write( "to solve for when y = 150, you need to solve the equation of:<BR>\n" );
document.write( ".485x^2 - 1.694x + .315 = 150<BR>\n" );
document.write( "the easiest way to solve this is to subtract 150 from both sides of the equation to get:<BR>\n" );
document.write( ".485x^2 - 1.694x - 149.685 = 0<BR>\n" );
document.write( "you would then use the quadratic formula to get the answer.<BR>\n" );
document.write( "that answer would be:<BR>\n" );
document.write( "x = -15.90803 or x = 19.400818<BR>\n" );
document.write( "since x can't be negative, the answer is 150 million users when x = 19.400818.<BR>\n" );
document.write( "year 19 equates to the year 2004 + 19 = 2023.<BR>\n" );
document.write( "year 6 equates to the year 2004 + 6 = 2010<BR>\n" );
document.write( "year 18 equates to the year 2004 + 18 = 2022.<BR>\n" );
document.write( " </SPAN>\n" );
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