Chapter 2.3, Problem 20E

The data in the table give sales revenue and costs and expenses for Continental Divide Mining for various years. Use this table in problem $20$ and $21$.

$\begin{array}{lll}\hfill & \text{Sales Revenue}\hfill & \text{costs and expenses}\hfill \\ \text{Year}\hfill & \text{(millions)}\hfill & \text{(millions)}\hfill \\ \text{2010}\hfill & \text{\$2}\text{.6155}\hfill & \text{\$2}\text{.4105}\hfill \\ \text{2011}\hfill & \text{2}\text{.7474}\hfill & \text{2}\text{.4412}\hfill \\ \text{2012}\hfill & \text{2}\text{.934}\hfill & \text{2}\text{.6378}\hfill \\ \text{2013}\hfill & \text{3}\text{.3131}\hfill & \text{2}\text{.9447}\hfill \\ \text{2014}\hfill & \text{9}\text{.9769}\hfill & \text{3}\text{.5344}\hfill \\ \text{2015}\hfill & \text{4}\text{.5494}\hfill & \text{3}\text{.8171}\hfill \\ \text{2016}\hfill & \text{4}\text{.8949}\hfill & \text{4}\text{.2587}\hfill \\ \text{2017}\hfill & \text{5}\text{.1686}\hfill & \text{4}\text{.8769}\hfill \\ \text{2018}\hfill & \text{4}\text{.9593}\hfill & \text{4}\text{.9088}\hfill \\ \text{2019}\hfill & \text{5}\text{.0913}\hfill & \text{4}\text{.6771}\hfill \\ \text{2020}\hfill & \text{4}\text{.7489}\hfill & \text{4}\text{.9025}\hfill \end{array}$

Assume that sales revenue for continental Divide Mining can be modelled b $R(t)=-0.031t^2+0.776t+0.179$

Where $t$ is the number of year past $2007$

Use the function to determine the year in which maximum revenue occurs and the maximum revenue it predicted.

Check the result from (a) against the data in the table.

Graph $R(t)$ and the data points from the table.

Write a sentence to describe how well the function fits the data.