The bar graph shows the average dormitory charges at public and private four-year U.S. colleges. Use the information displayed by the graph to solve Exercises 65–66.

a. Use the numbers shown by the bar graph to find the total dormitory charges at private colleges for a four-year period from the school year ending in 2010 through the school year ending in 2013.

b. The model a_n = 198n + 5037 describes the dormitory charges at private colleges in academic year n, where n = 1 corresponds to the school year ending in 2010, n = 2 to the school year ending in 2011, and so on. Use this model and the formula for S_n to find the total dormitory charges at private colleges for a four-year period from the school year ending in 2010 through the school year ending in 2013. How does this compare with the actual sum you obtained in part (a)?

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Dormitory Charges $7000 $6000 $5000 $4000 $3000 $2000 $1000 4565 5249 2010 Average Dormitory Charges at Four-Year U.S. Colleges Public Institutions Private Institutions... 4824 5413 5046 5629 2011 2012 Ending Year in the School Year 5241 5837 2013