The average cost of tuition and fees at public four year colleges in the United States can be modeled by the formula $$T = 165x+2771,$$ where T represents the average cost of tuition and fees for the school year ending x years after 1996. Use the formula to determine the year when tuition and fees at public U.S. colleges average $4586.
(Note: Give the year. For example, if you calculate that the answer is 9 years after 1996, then enter 2005 .)

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