document.write( "Question 1196259: In 2007, the population of a certain country per square mile of land area was 83. In 2000, the person per square mile population was 79.5 . Assume the relationship between years and persons per square mile is a linear relationship.\r
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\n" ); document.write( "In 2007, the population of a certain country per square mile of land area was 83.
\n" ); document.write( "In 2000, the person per square mile population was 79.5 .
\n" ); document.write( "Assume the relationship between years and persons per square mile is a linear relationship.\r
\n" ); document.write( "\n" ); document.write( "(a) Write an equation, in slope-intercept form, describing the relationship between year
\n" ); document.write( "and persons per square mile. Use ordered pairs of the form (x,y) ,
\n" ); document.write( "where x is the number of years past 2000 and y is persons per square mile.
\n" ); document.write( "(b) Use this equation to predict the person per square mile population in 2020 .
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document.write( "Slope-intercept form is  y = mx + b.    (1)\r\n" );
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document.write( "In this equation, \"m\"  is the slope.\r\n" );
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document.write( "The ordered pairs are (0,79.5) and (7,83).\r\n" );
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document.write( "In pair (0,79.5), the zero represents the current (starting) year 2000.\r\n" );
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document.write( "In pair (7,83), the \"7\" represents the year 2007, 7 years after 2000.\r\n" );
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document.write( "The slope is the ratio  m =  =  =  = 0.5.\r\n" );
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document.write( "The slope 0.5 means that every year, the population density per square mile rises \r\n" );
document.write( "with the rate of 0.5 of a person per square mile per year.\r\n" );
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document.write( "So, we just know that in formula (1) m = 0.5.\r\n" );
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document.write( "The value of \"b\" in formula (1) is the starting population of 79.5 in the starting year of 2000.\r\n" );
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document.write( "So, the formula now, in its final form is y = 0.5*x + 79.5,    (2)\r\n" );
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document.write( "and it represents/expresses the population density per square mile x years after 2000.\r\n" );
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document.write( "To predict the population density in the year 2020, first calculate the number of years from the year 2000.\r\n" );
document.write( "It is  2020 - 2000 = 20.\r\n" );
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document.write( "Now substitute x= 20 into the formula (2).  You will get\r\n" );
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document.write( "    y = 0.5*20 + 79.5 = 10 + 79.5 = 89.5 persons per square mile.\r\n" );
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