Question

The data in the table give sales revenues and costs and expenses for a mining company for various years.

Year		Sales Revenue (millions)		Costs and Expenses (millions)
2006		$1.6928		$2.4105
2007		2.5097		2.4412
2008		2.8313		2.6378
2009		2.6936		2.9447
2010		3.3802		3.5344
2011		3.5507		3.8171
2012		3.7456		4.2587
2013		4.0797		4.8769
2014		4.3329		4.9088
2015		4.4070		4.6771
2016		3.9759		4.9025

Assume that sales revenue for the company can be modeled by

R(t) = −0.031t² + 0.686t + 0.179

where t is the number of years past 2003.

(a) Use the function to determine the year in which maximum revenue occurs.


Determine the maximum revenue the function predicts. (Round your answer to two decimal places.)
$  million

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

Answer 1

Using the function, the revenue in each year are :

2006 : 1.958

2007 : 2.427

2008 : 2.834

2009 : 3.179

2010 : 3.462

2011 : 3.683

2012 : 3.842

2013 : 3.939

2014 : 3.974

2015 : 3.947

2016 : 3.858

a) We can find that the maximum revenue the function predicts is $3.974 million $3.97 million, which is in the year 2014.

b) In the table, the maximum revenue is obtained in the year 2015. There is a difference of $0.433 million in the maximum revenue value obtained using the function and that from the table data.