The bar graph shows the average cost of tuition and fees at private four-year co

Question

The bar graph shows the average cost of tuition and fees at private four-year colleges in the United States. Source: The College Board. Here are two mathematical models for the data shown in the graph. In each formula, T represents the average cost of tuition and fees at private U.S. colleges for the school year ending x years after 2000. T = 1157x + 14.961 T = 21x62 + 862x + 15,552 Use this information to solve Exercises 67-68. a. Use each model to find the average cost of tuition and fees at private US. colleges for the school year ending in 2012. By how much does each model underestimate or overestimate the actual cost shown for the school year ending in 2012? b. Use model 1 to determine when tuition and fees at private four-year colleges will average $39.258.

Explanation / Answer

a) Model 1:

In 2012, we get x=12

So, T(12)=1157*12+14961= 28845

Model 2:

T(12)=21*(12)^2+862*12+15552=28920

The average cost of Tuition and fees for 2012, from the graph we have as 29056

So, model 1 underestimate =29056-28845=211

Model 2, underestimate=29056-28920=136

b) From model 1, we have, T(x)=1157*x+14961

When, T(x)=39258, we have,

39258=1157*x+14961

1157x=39258-14961

1157x=24297

x=24297/1157

x=21

So, the cost will average in year 2021 (2000+21).

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