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)=962x + 3315 and g(x)=3856e^{0.131x} 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. (round to the nearest dollar as needed.) b. according to the exponential model, what was the average cost of room and board at public four - year colleges for the school year ending in 2013? the average cost in 2013 was $5712. (round to the nearest dollar as needed.) 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 is years after 2010, for 2013, $x = 2013 - 2010=3$.

Step2: Calculate the value from the linear - model f(x)

Given $f(x)=962x + 3315$, substitute $x = 3$ into it: $f(3)=962\times3+3315=2886 + 3315=6201$.

Step3: Calculate the value from the exponential - model g(x)

Given $g(x)=3856e^{0.131x}$, substitute $x = 3$ into it: $g(3)=3856e^{0.131\times3}=3856e^{0.393}$. Using a calculator, $e^{0.393}\approx1.4817$, so $g(3)=3856\times1.4817\approx5712$.

Step4: Compare with the actual value from the bar - graph

From the bar - graph, the actual value for public colleges in 2013 is 5363. The error for the linear model is $|6201 - 5363|=838$. The error for the exponential model is $|5712 - 5363| = 349$. Since 349<838, the exponential model is better.

Answer:

A. The exponential model is better.