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 + 3370 ) and ( g(x)=3855e^{0.137x} ) 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 2017?
○ a. the linear model is better.
○ b. the exponential model is better.

Explanation:

Step1: Calculate \( f(x) \) for \( x = 7 \) (since \( 2017 - 2010=7 \))

Substitute \( x = 7 \) into \( f(x)=958x + 3370 \).

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Step2: Calculate \( g(x) \) for \( x = 7 \)

Substitute \( x = 7 \) into \( g(x)=3855e^{0.137x} \).

$$
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$$

Step3: Compare the model values with the actual value (public college cost in 2017 is \( 10222 \))

The difference for \( f(x) \): \( |10222 - 10076|=146 \)
The difference for \( g(x) \): \( |10222-10061.55| = 160.45 \)

Answer:

A. The linear model is better.