document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=182660>Question 182660</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The national cost C in billions of dollars for dental services can be modeled by the linear equation C= 2.85n + 3052, where n is the number of years since 1990.<BR>\n" );
document.write( "a) find and interpret the C-intercept for the line<BR>\n" );
document.write( "b) find and interpret the n-intercept for the line<BR>\n" );
document.write( "c) graph the line for n ranging from 0 through 20<BR>\n" );
document.write( "d) if this trend continues, then in what year will the cost of dental services reach 100 billion?\r<BR>\n" );
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document.write( "This is what I have so far for an answer:\r<BR>\n" );
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document.write( "I tried to solve for C. I began by subtracting 1990 from this current year 2009 which gave me 19, so n=19. Then I was able to solve for C.<BR>\n" );
document.write( "C= 2.85(19) + 3052<BR>\n" );
document.write( "C= 54.15 + 30.52<BR>\n" );
document.write( "C= 84.67\r<BR>\n" );
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document.write( "a) n=0, then C=2.85(0) + 30.52. C-intercept is (0, 30.52)\r<BR>\n" );
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document.write( "b) C=0, then 2.85n + 30.52 = 0 Here's my work for this equation: <BR>\n" );
document.write( "   2.85n + 30.52 - 30.52 = 0 -30.52<BR>\n" );
document.write( "   2.85n/2.85 = -30.52/2.85<BR>\n" );
document.write( "   n=-10.70<BR>\n" );
document.write( "   n-intercept is (-10.70, 0) or is the n-intercept (19, 84.67)? \r<BR>\n" );
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document.write( "d)I think I have to substitute C for 84.67 which will allow me to solve the   equation for n. Below is what I did.<BR>\n" );
document.write( "  C= 2.85n + 30.52<BR>\n" );
document.write( "  8467= 2.85n + 30.52<BR>\n" );
document.write( " -30.52       - 30.52<BR>\n" );
document.write( "  54.15= 2.85n<BR>\n" );
document.write( "  54.15/2.85 = 2.85n/2.85<BR>\n" );
document.write( "  n=19<BR>\n" );
document.write( "So will the year be 2019 since n=19?      <BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #137133 by </B><A HREF=/tutors/aboutme.mpl?userid=Mathtut><B>Mathtut(3670)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Mathtut><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=137133\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A) Find and interpret the C-intercept for the line<BR>\n" );
document.write( "C = 2.85n + 30.52<BR>\n" );
document.write( ":<BR>\n" );
document.write( "C = 2.85(0) + 30.52<BR>\n" );
document.write( "C = 30.52......(0,30.52)<BR>\n" );
document.write( "At zero years, the C-intercept is at $30.52 billion.<BR>\n" );
document.write( "B)Find and interpret the n-intercept for the line<BR>\n" );
document.write( "C = 2.85n + 30.52<BR>\n" );
document.write( "0 = 2.85n + 30.52<BR>\n" );
document.write( "-30.52 = 2.85n<BR>\n" );
document.write( "-30.52/285 = n<BR>\n" );
document.write( "-10.70= n   (-10.70,0) remember in an x intercept(n in our case) y is always zero.<BR>\n" );
document.write( "n intercept means in 1979 , the cost was zero.<BR>\n" );
document.write( "C)Graph the line for n ranging from 0 through 20<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+800%2C+600%2C+-2%2C+20%2C+-5%2C+90%2C+2.85x+%2B+30.52+%29+ ALIGN=MIDDLE  ALT=\"+graph%28+800%2C+600%2C+-2%2C+20%2C+-5%2C+90%2C+2.85x+%2B+30.52+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "D If this trend continues, then in what year will the <BR>\n" );
document.write( "cost of dental services reach 100 billion?<BR>\n" );
document.write( "C = 2.85n + 30.52<BR>\n" );
document.write( "100 = 2.85n + 30.52<BR>\n" );
document.write( "69.48 = 2.85n<BR>\n" );
document.write( "About 24.37 years later:<BR>\n" );
document.write( "so between 24 and 25 years it will reach 100 billion<BR>\n" );
document.write( "Year: 2014-2015<BR>\n" );
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