document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=978523>Question 978523</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The consumer price index (CPI) is calculated by averaging the prices of various items after assigning a weight to each item. The following table gives the consumer price indexes for selected years from 1940 through 2008, reflecting buying patterns of all urban consumers, with x representing years past 1900.<BR>\n" );
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document.write( "1940		14	1990		130.7<BR>\n" );
document.write( "1950		24.1	2000		172.2<BR>\n" );
document.write( "1960		29.6	2005		195.3<BR>\n" );
document.write( "1970		38.8	2008		215.3<BR>\n" );
document.write( "1980		82.4			<BR>\n" );
document.write( "(a) Find an equation that models these data. (Round your coefficients to three decimal places.)<BR>\n" );
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document.write( "Incorrect: Your answer is incorrect.<BR>\n" );
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document.write( "(b) Use the model to predict the consumer price index in 2017. (Round your answer to one decimal place.)<BR>\n" );
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document.write( "(c) According to the model, during what year will the consumer price index pass 300?<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #599897 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=599897\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let\r<BR>\n" );
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document.write( "x = number of years since 1900 (x = 0 represents 1900, x = 1 represents 1901, etc)<BR>\n" );
document.write( "y = CPI for a given year x years after 1900\r<BR>\n" );
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document.write( "CPI = Consumer Price Index\r<BR>\n" );
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document.write( "<tr><th>Year</th><th>CPI</th></tr><tr><TD >40</TD><TD >14</TD></tr><tr><TD >50</TD><TD >24.1</TD></tr><tr><TD >60</TD><TD >29.6</TD></tr><tr><TD >70</TD><TD >38.8</TD></tr><tr><TD >80</TD><TD >82.4</TD></tr><tr><TD >90</TD><TD >130.7</TD></tr><tr><TD >100</TD><TD >172.2</TD></tr><tr><TD >105</TD><TD >195.3</TD></tr><tr><TD >108</TD><TD >215.3</TD></tr>\n" );
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document.write( "a)\r<BR>\n" );
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document.write( "Use a calculator (like a TI83) or excel to find the equation of the regression line.\r<BR>\n" );
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document.write( "If you have neither, then use this <a  rel=nofollow HREF=\"http://www.alcula.com/calculators/statistics/linear-regression/\">free online calculator</a> and it will get the job done.\r<BR>\n" );
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document.write( "The regression line is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=3.096940216896x-141.63877471977 ALIGN=MIDDLE  ALT=\"y=3.096940216896x-141.63877471977\"   DISABLED_style= \"max-width:90%; height:auto;\" > (this is approximate)\r<BR>\n" );
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document.write( "b)\r<BR>\n" );
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document.write( "Plug in x = 117 (Note: 2017 - 1900 = 117) to find the predicted CPI in 2017\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=3.096940216896%2A117-141.63877471977 ALIGN=MIDDLE  ALT=\"y=3.096940216896%2A117-141.63877471977\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=220.703230657062 ALIGN=MIDDLE  ALT=\"y=220.703230657062\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=220.7 ALIGN=MIDDLE  ALT=\"y=220.7\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "I rounded the result to 1 decimal place because all of the other CPI values are shown accurate to 1 decimal place.\r<BR>\n" );
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document.write( "The predicted CPI in the year 2017 is <font color=\"red\">220.7</font>\r<BR>\n" );
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document.write( "c)\r<BR>\n" );
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document.write( "Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+300 ALIGN=MIDDLE  ALT=\"y+=+300\"   DISABLED_style= \"max-width:90%; height:auto;\" > and solve for x\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=300=3.096940216896x-141.63877471977 ALIGN=MIDDLE  ALT=\"300=3.096940216896x-141.63877471977\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=300%2B141.63877471977=3.096940216896x ALIGN=MIDDLE  ALT=\"300%2B141.63877471977=3.096940216896x\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Round to the nearest whole number to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+143 ALIGN=MIDDLE  ALT=\"x+=+143\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "It will take 143 years for the CPI to pass 300. So the CPI will pass 300 in the year 1900+143 = <font color=\"red\">2043</font> </SPAN>\n" );
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