The average cost of tuition and fees at public four year colleges in the United States can be modeled by the formula

T (x) = 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.)

Year 2007

Step-by-step explanation:

Given that, the average cost of tuition and fees of a colleges:

T (x) = 165 x + 2771

where T represents the average cost of tuition and fees for the school year ending x years after 1996.

We need to find x years after 1996 when T = $4,586.

So, substitute with T at the formula of T (x)

∴ 4,586 = 165 x + 2771

Solve for x

∴ 165 x = 4,586 - 2,771 = 1,815

∴ x = 1,815/165 = 11 years

So, the year when tuition and fees average $4586 is 1996 + 11 = 2007