SOLUTION: The number (C) of U.S Supreme Court cases on docket from 1996 to 2001 can be approximated by the linear equation: C= 344.3t + 5400, 6<_t <_11 where t is the year, with t=6 corres

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Question 180660: The number (C) of U.S Supreme Court cases on docket from 1996 to 2001 can be approximated by the linear equation:
C= 344.3t + 5400, 6<_t <_11
where t is the year, with t=6 corresponding to 1996. If this linear pattern continues, in what year will the number of U.S. Supreme Court cases reach 11,000?
Please help. I don't even know where to start! Thanks.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Start with your equation.
C=+344.3t+%2B+5400 for 6%3C=t%3C=11
Find t when C=11000.
You assume that the equation stays linear when t%3E11.
344.3t+%2B+5400=11000
344.3t=5600
t=16.3
Since t=6 is the year 1996, then year t=16 would be year 2006.
The leftover 0.3 year would get you to roughly 3rd or 4th month of 2006.
I'm not sure if you need to be that exact or if you can say between 2006 and 2007.