Question 158875: The United States is China's largest export market. Imports from China grew from about 82 billion dollars in 1999 to 152 billion dollars in 2003. Let x=0 correspond to 1990, and estimate the amount of imports in 2006.
Answer by gonzo(654)   (Show Source):
You can put this solution on YOUR website! 1999 = 82 billion dollars
2003 = 152 billion dollars
1990 = 0 billion dollars
estimate 2006.
if i read this problem, correctly, your sequence of imports is
1990 = 0
1999 = 82
2003 = 152
2006 = ?
taking a linear average from 1990 to 2006, we would get an equation that states
y = change in value of imports from 1990 to 2003 / change in number of years from 1990 to 2003.
y would = (152-0)/(2003-1990) which would equal 11.69230769 billion dollars increase per year.
2006 imports would equal 2003 imports plus (11.69230769 * ( 2006-2003) which would equal 152 billion plus (3*11.69 billion) which would equal 187.0769231 billion dollars.
this is a straight line overall average from 1990 to 2006
if you were to take the most recent trends rather than the overall average, however, you would look for history from 1999 to 2003 which would probably yield a different projection.
working it through yields the following.
taking a linear average from 1999 to 2006, we would get an equation that states
y = change in value of imports from 1999 to 2003 / change in number of years from 1999 to 2003.
y would = (152-82)/(2003-1999) which would equal 17.5 billion dollars increase per year.
2006 imports would equal 2003 imports plus (17.5 * (2006-2003) which would equal 152 + (17.5*3) = 204.5 billion dollars a year.
this is based on the more recent activity which showed a much higher average yearly change between 1999 and 2003 then the overall from 1990 to 2003.
bottom line is if you did a straight line average from 1990 to 2003 you would get 187 billion in 2006 and if you did a straight line average from 1999 to 2003 you would get 204 billion in 2006.
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