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)=957x + 3176 ) and ( g(x)=3853e^{0.132x} ). 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 2015?
a. the linear model is better.
b. the exponential model is better.

Explanation:

Step1: Calculate the value of the linear model \( f(x) \) for \( x = 5 \) (since \( 2015 - 2010=5 \))

Substitute \( x = 5 \) into \( f(x)=957x + 3176 \)

$$
LATEXBLOCK0
$$

Step2: Calculate the value of the exponential model \( g(x) \) for \( x = 5 \)

Substitute \( x = 5 \) into \( g(x)=3853e^{0.132x} \)

$$
LATEXBLOCK1
$$

Step3: Compare the model values with the actual value from the bar - graph

From the bar - graph, the actual value for public four - year colleges in 2015 is \( 7592 \).
The error for the linear model: \(|7961 - 7592|=369\)
The error for the exponential model: \(|7455 - 7592| = 137\)

Answer:

B. The exponential model is better.