Application Exercises The bar graph shows the average cost of tuition and fees a

Question

Application Exercises 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 2014. By how much does each model underestimate or overestimate the actual cost shown for the school year ending in 2014? b. Use model 1 to determine when tuition and fees at private four-year colleges will average $36,944.

Explanation / Answer

(a)

Model:1

T = 1157x + 14961

We need to find average cost of tuition for the school year ending in 2014.

Hence x = 14 years.

So T = 1157(14)+14961

= $31,159

Actual cost given in chart is $31,701

So difference is $31,701-$31,159=$542 ( lower than actual cost)

Model:2

T= 21x2+862x+15552

x= 14

Hence

T= 21(14)2+862(14)+15552

= $31,736

Difference is : $31,736-$31701= $35( higher than actual cost)

(b)

By model1

T= 1157x+14961

T= $36944

i.e. 36944= 1157(x)+14961

x = 19

Hence it will be in 2000+19= 2019

In 2019 , the tuition and fees at private colleges will average $36944.

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