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 + 3169 and g(x)=3880e^{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. (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 the number of years after 2010, for 2013, $x = 2013 - 2010=3$.

Step2: Calculate the value from the linear - model

Substitute $x = 3$ into $f(x)=958x + 3169$.
$f(3)=958\times3 + 3169=2874+3169 = 6043$.

Step3: Calculate the value from the exponential - model

Substitute $x = 3$ into $g(x)=3880e^{0.132x}$.
$g(3)=3880e^{0.132\times3}=3880e^{0.396}$.
Using a calculator, $e^{0.396}\approx1.485$, so $g(3)=3880\times1.485 = 3880\times\frac{1485}{1000}=3880\times1.485 = 5761.8\approx5762$.

Step4: Find the actual value from the bar - graph

From the bar - graph, the average cost of room and board at public four - year colleges for the school year ending in 2013 is $5388$.

Step5: Calculate the errors

The error for the linear model, $|5388 - 6043|=655$.
The error for the exponential model, $|5388 - 5762| = 374$.
Since $374<655$, the exponential model has a smaller error.

Answer:

A. The exponential model is better.