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) 967x + 3469 and g(x) 3950 e134x 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. Average Cost of Room and Board at Four-Year Colleges ublic Colleges 12000- Private College 10000- 8O00-49520 7615 5 *0,64 2011 2013 2015 2017 Ending Year School Year According to the linear model, what was the average cost of room and board at public four-year colleges for the school year ending in 2015? a. The average cost in 2015 was (Round to the nearest dollar needed.) as 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 2015? The average cost in 2015 was S (Round to the nearest dollar as needed.) c. Which function is a better model for the data for the school year ending in 2015? O A. The exponential model is better O B. The linear model is better.

Answer 1

x is the number of year after 2010.

So year ending 2015 .x=2015-2010=5.

X=5 in both models

a)

Linear model in given model is

f(x)=967*x+3469.

To find average cost for public school for year ending 2015 by linear model ,find f(5)

f(5)=967*5+3469=8304

Cost is 8304

b)

Exponential model is

g(x)3950 *e.134

To find average cost for public school for year ending 2015 by exponential model ,find g(5)

g(5) 3950 e0.134+5 7719.237417

On rounding we get cost as 7719

C) exponential model is better

From graph it is clear that average cost for public colleges for 2015 is 7615.

Exponential model gives answer nearer to it