document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=249990>Question 249990</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Wow I don't understand this it says in 1990, the life expectancy of males was 64.7 years. In 1995 it was 67.8 years, let E represent the life expectancy in year t and let t represent the number of years since 1990.<BR>\n" );
document.write( "E(t)=?t+? and round to nearest tenth<BR>\n" );
document.write( "Use the function to predict life expectancy in 2005<BR>\n" );
document.write( "E(15)=? round to the nearest tenth<BR>\n" );
document.write( "Thanks for any and all help </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #182050 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=182050\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1990 E(t) = 64.7<BR>\n" );
document.write( "1995 E(t) = 67.8\r<BR>\n" );
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document.write( "your equation is:\r<BR>\n" );
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document.write( "E(t) = m*t + b\r<BR>\n" );
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document.write( "m = slope of your line (I'm presuming they are asking for a straight line projection.\r<BR>\n" );
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document.write( "b = the y-intercept which is the value of E(t) when t = 0\r<BR>\n" );
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document.write( "In 1990, t = 0 because 1990 is your base year.<BR>\n" );
document.write( "In 1995, t = 5 because 1995 minus 1990 = 5<BR>\n" );
document.write( "In 2005, t = 15 because 2005 minus 1990 = 15\r<BR>\n" );
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document.write( "You have 2 data points to work with.\r<BR>\n" );
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document.write( "They are:\r<BR>\n" );
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document.write( "E(0) = 64.7<BR>\n" );
document.write( "E(5) = 67.8\r<BR>\n" );
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document.write( "E(0) means the value of E(t) when t = 0.<BR>\n" );
document.write( "E(5) means the value of E(t) when t = 5.\r<BR>\n" );
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document.write( "you can use these points to find the slope of your line.\r<BR>\n" );
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document.write( "slope of your line is equal to ((E(5) - E(0))/(5-0).  \r<BR>\n" );
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document.write( "This becomes:\r<BR>\n" );
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document.write( "slope of your line is equal to ((67.8) - (64.7)) / 5 = 3.1/5 = .62\r<BR>\n" );
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document.write( "replace m with .62 and your equation becomes:\r<BR>\n" );
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document.write( "E(t) = .62 * t + b\r<BR>\n" );
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document.write( "Take either of your data points and substitute in this equation to solve for b.\r<BR>\n" );
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document.write( "Use E(t) = 64.7 when t = 0\r<BR>\n" );
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document.write( "64.7 = .62 * 0 + b which becomes 64.7 which equals b in your equation.\r<BR>\n" );
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document.write( "your equation becomes:\r<BR>\n" );
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document.write( "E(t) = .62 * t + 64.7\r<BR>\n" );
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document.write( "In 2005, t will equal 15.\r<BR>\n" );
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document.write( "Substitute for t in the equation to get:\r<BR>\n" );
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document.write( "E(15) = .62 * 15 + 64.7\r<BR>\n" );
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document.write( "Solve for E(15) to get:\r<BR>\n" );
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document.write( "E(15) = 74\r<BR>\n" );
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document.write( "To graph this equation, replace E(t) with y and replace t with x to get:\r<BR>\n" );
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document.write( "y = .62 * x + 64.7\r<BR>\n" );
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document.write( "There's a horizontal line at y = 74 to show you that the graph of the equation intersect this line when x = 15.  x = 15 in the graph is the same as t = 15 in the original equation.\r<BR>\n" );
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document.write( "graph of your equation looks like this:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28600%2C600%2C-5%2C20%2C-10%2C100%2C.62%2Ax+%2B+64.7%2C+74%29 ALIGN=MIDDLE  ALT=\"graph%28600%2C600%2C-5%2C20%2C-10%2C100%2C.62%2Ax+%2B+64.7%2C+74%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
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