Chapter 8.1, Problem 69E

The bar graph at the top of the next column shows the average number of hours per day that U.S. adult users spent on digital media (desktop/laptop, mobile, and other devices) from 2008 through 2014.

Let a_n represent the average number of hours per day that U.S. adult users spent on digital media n years after 2007.

a. Use the numbers given in the graph to find and interpret $\frac{1}{7}{\displaystyle \underset{i=1}{\overset{7}{\sum }}{a}_i}$. Round to the nearest tenth of an hour.

b. The finite sequence whose general term is

a_n = 0.5n + 2,

where n = 1, 2, 3, 4, 5, 6, 7, models the average number of hours per day that U.S. adult users spent on digital media n years after 2007. Use this model to find $\frac{1}{7}{\displaystyle \underset{i=1}{\overset{7}{\sum }}{a}_i}$. Does this underestimate or overestimate the rounded value you obtained in part (a)? By how much?