document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=285659>Question 285659</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Life Span Some scientists believe there is a limit to how<BR>\n" );
document.write( "long humans can live.* One supporting argument is that<BR>\n" );
document.write( "during the last century, life expectancy from age 65 has<BR>\n" );
document.write( "increased more slowly than life expectancy from birth, so<BR>\n" );
document.write( "eventually these two will be equal, at which point, according<BR>\n" );
document.write( "to these scientists, life expectancy should increase no<BR>\n" );
document.write( "further. In 1900, life expectancy at birth was 46 yr, and life<BR>\n" );
document.write( "expectancy at age 65 was 76. In 2000, these figures had<BR>\n" );
document.write( "risen to 76.9 and 82.9, respectively. In both cases, the<BR>\n" );
document.write( "increase in life expectancy has been linear. Using these<BR>\n" );
document.write( "assumptions and the data given, find the maximum life<BR>\n" );
document.write( "expectancy for humans. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #207169 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=207169\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Some scientists believe there is a limit to how long humans can live.<BR>\n" );
document.write( " One supporting argument is that during the last century, life expectancy from<BR>\n" );
document.write( " age 65 has increased more slowly than life expectancy from birth, so <BR>\n" );
document.write( "eventually these two will be equal, at which point, according to these<BR>\n" );
document.write( " scientists, life expenctancy should increase no further. <BR>\n" );
document.write( "In 1900, life expectancy at birth was 46yr, and life expectancy at age 65 was 76.<BR>\n" );
document.write( " In 2000, these figures had risen to 76.9 and 82.9 , respectively.<BR>\n" );
document.write( " IN both cases, the increase in life expectancy has been linear.<BR>\n" );
document.write( " Using these assumptions and the data given, find the maximum life expectancy for humans.<BR>\n" );
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document.write( "Let x = number of yrs from 1900 (1900 = 0 and 2000 = 100)<BR>\n" );
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document.write( "Let y = yrs of life expected<BR>\n" );
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document.write( "Determine the \"from birth\" equation<BR>\n" );
document.write( "x1 = 0; y1 = 46<BR>\n" );
document.write( "x2 = 100; y2 = 76.9<BR>\n" );
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document.write( "Find the slope: m = (y2-y1)/(x2-x1)<BR>\n" );
document.write( "m = (76.9 - 46)/(100-0)  = 30.9/100 = .309 is the slope<BR>\n" );
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document.write( "Find the equation using y - y1 = m(x-x1)<BR>\n" );
document.write( "y - 46 = .309(x - 0)<BR>\n" );
document.write( "y = .309x + 46<BR>\n" );
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document.write( "Determine the \"from age 65\" equation (green):<BR>\n" );
document.write( "x1 = 0; y1 = 76<BR>\n" );
document.write( "x2 =100; y2 = 82.9<BR>\n" );
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document.write( "Find the slope:<BR>\n" );
document.write( "m = (82.9-76)/(100 - 0) = 6.9/100 = .069 is the slope<BR>\n" );
document.write( "Find the equation:<BR>\n" );
document.write( "y - 76 = .069(x - 0)<BR>\n" );
document.write( "y = .069x + 76<BR>\n" );
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document.write( "Max life expectancy is said to occur when these two lines intersect:<BR>\n" );
document.write( "Age = vertical axis, year = horizontal<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+200%2C+-20%2C+150%2C+-10%2C+110%2C+.309x%2B46%2C+.069x%2B+76%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+200%2C+-20%2C+150%2C+-10%2C+110%2C+.309x%2B46%2C+.069x%2B+76%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "To solve, put equations into the standard form to solve:<BR>\n" );
document.write( "-.309x + y = 46<BR>\n" );
document.write( "-.069x + y = 76<BR>\n" );
document.write( "-----------------subtracting eliminates y<BR>\n" );
document.write( "-.24x = -30<BR>\n" );
document.write( "    x = -30/-.24<BR>\n" );
document.write( "    x = 125 yrs,  (the year 2025)<BR>\n" );
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document.write( "Find the actual age this occurs, find y:<BR>\n" );
document.write( "-.069(125) + y = 76<BR>\n" );
document.write( "-8.625 + y = 76 <BR>\n" );
document.write( "y = 76 + 8.625<BR>\n" );
document.write( "y = 84.625 max age<BR>\n" );
document.write( ":\r<BR>\n" );
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document.write( " <BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );