document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=331487>Question 331487</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I have asked for help on this story problem before however I have never heard back so I am still need of some help with solving this story problem.\r<BR>\n" );
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document.write( "In 1991 the life expectancy of males in a certain country was 63.2 years. In 1996 it was 65.7 years. Let E represent the life expectancy in year t, and let + represent the number of years since 1991.\r<BR>\n" );
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document.write( "The linear function E(t) that fits the data is E)t)=_____t + _____.\r<BR>\n" );
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document.write( "Use the function to predict the life expectancy of males in 2006.\r<BR>\n" );
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document.write( "E (15)= _____ and round to the nearest tenth.\r<BR>\n" );
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document.write( "Thanks for your help :o) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #237605 by </B><A HREF=/tutors/aboutme.mpl?userid=vleith><B>vleith(2983)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=vleith><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=237605\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Use the info provided to create a linear model of Life Expenctency.\r<BR>\n" );
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document.write( "You are given two points. With that data you have enough information to create the equation for a line.\r<BR>\n" );
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document.write( "First let's find the slope of the line<BR>\n" );
document.write( "Slope = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y%5B2%5D+-+y%5B1%5D%29+%2F+%28x%5B2%5D+-+x%5B1%5D%29 ALIGN=MIDDLE  ALT=\"%28y%5B2%5D+-+y%5B1%5D%29+%2F+%28x%5B2%5D+-+x%5B1%5D%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "You are given the two data points (1991,63.2) and (1996, 65.7)<BR>\n" );
document.write( "So the slope is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2865.7-63.2%29%2F%281996+-+1991%29 ALIGN=MIDDLE  ALT=\"%2865.7-63.2%29%2F%281996+-+1991%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2.5%2F5+=+1%2F2 ALIGN=MIDDLE  ALT=\"2.5%2F5+=+1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The problem says to model the Life Expectancy where t is the 'number of years since 1991\"<BR>\n" );
document.write( "So<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=E%28t%29+=+%281%2F2%29+t+%2B+63.2 ALIGN=MIDDLE  ALT=\"E%28t%29+=+%281%2F2%29+t+%2B+63.2\"   DISABLED_style= \"max-width:90%; height:auto;\" > that uses the slope we found above as the rate of change year to year. It also uses the expectency in the year 1991 as the starting point.<BR>\n" );
document.write( "Check this now. In year 1991, t = 1991-1991 = 0. So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=E%280%29+=+0%2At+%2B+63.2+=+63.2 ALIGN=MIDDLE  ALT=\"E%280%29+=+0%2At+%2B+63.2+=+63.2\"   DISABLED_style= \"max-width:90%; height:auto;\" > which is correct<BR>\n" );
document.write( "IN 1996, t = 1996-1991 = 5. So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=E%285%29+=+%281%2F2%29%2A5+%2B+63.2+=+2.5%2B63.2+=+65.7 ALIGN=MIDDLE  ALT=\"E%285%29+=+%281%2F2%29%2A5+%2B+63.2+=+2.5%2B63.2+=+65.7\"   DISABLED_style= \"max-width:90%; height:auto;\" > which is correct\r<BR>\n" );
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document.write( "You are then asked to use the equation to extrapolate the data to the year 2006<BR>\n" );
document.write( "So, 2006-1991 = 15<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=E%2815%29+=+15%2F2+%2B+63.2+=+7.5+%2B+63.2+=+70.7 ALIGN=MIDDLE  ALT=\"E%2815%29+=+15%2F2+%2B+63.2+=+7.5+%2B+63.2+=+70.7\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Again, this is just a model. There is nothing to suggest that Life expectency is linear. But that is all the data you have, so you have to go with that.\r<BR>\n" );
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document.write( "Make sense?<BR>\n" );
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