Question

the bar graph on the right shows the average cost of room and board at four - year public and private colleges for four selected years from 2011 through 2017. the data can be modeled by ( f(x)=958x + 3486 ) and ( g(x)=3850e^{0.139x} ) in which ( f(x) ) and ( g(x) ) represent the average cost of room and board at public four - year colleges in the school year ending ( x ) years after 2010. use these functions to complete parts (a) through (c) below.

c. which function is a better model for the data for the school year ending in 2013?

a. the exponential model is better.

b. the linear model is better.

Explanation:

Step1: Determine the value of \(x\) for 2013

Since \(x\) represents years after 2010, for 2013, \(x = 2013 - 2010=3\).

Step2: Calculate \(f(3)\) (linear model)

Substitute \(x = 3\) into \(f(x)=958x + 3486\).

$$
LATEXBLOCK0
$$

Step3: Calculate \(g(3)\) (exponential model)

Substitute \(x = 3\) into \(g(x)=3850e^{0.139x}\).

$$
LATEXBLOCK1
$$

Step4: Compare with the actual value

From the bar - graph, the actual value for public colleges in 2013 is \(5205\).
The difference for the linear model: \(|6360 - 5205|=1155\).
The difference for the exponential model: \(|5840.45 - 5205| = 635.45\).

Answer:

A. The exponential model is better.