Chapter 4, Problem 31RE

(a)

To determine

Whether the model will be fitted in the data for the period $2004-2013$ when the table representing the net profits P (in millions of dollars) earned by Express Scripts during the period $2004-2013$ is as follows:

Year	$2004$	$2005$	$2006$	$2007$	$2008$	$2009$	$2010$	$2011$	$2012$	$2013$
Profit	$300.1$	$388.1$	$468.7$	$620.6$	$779.6$	$826.5$	$1204.6$	$1275.8$	$1340.5$	$1898.2$

The net profit P is given by the model as,

$P=147.8e^{0.196t}$

Where, t represents the year in which $t=4$ corresponds to $2004$.

(b)

To determine

To calculate: The linear model for the provided data and determine whether the linear model will be fitted in the data for the period $2004-2013$ and also determine the best fit model from the given exponential model and the obtained linear model when the table representing the net profits P (in millions of dollars) earned by Express Scripts during the period $2004-2013$ is as follows:

Year	$2004$	$2005$	$2006$	$2007$	$2008$	$2009$	$2010$	$2011$	$2012$	$2013$
Profit	$300.1$	$388.1$	$468.7$	$620.6$	$779.6$	$826.5$	$1204.6$	$1275.8$	$1340.5$	$1898.2$

The net profit P is given by the model as,

$P=147.8e^{0.196t}$

Where, t represents the year in which $t=4$ corresponds to $2004$.

(c)

To determine

To calculate: The net profit of the company in the year $2018$ by using the model obtained in part (b) and the provided model when the table representing the net profits P (in millions of dollars) earned by Express Scripts during the period $2004-2013$ is as follows:

Year	$2004$	$2005$	$2006$	$2007$	$2008$	$2009$	$2010$	$2011$	$2012$	$2013$
Profit	$300.1$	$388.1$	$468.7$	$620.6$	$779.6$	$826.5$	$1204.6$	$1275.8$	$1340.5$	$1898.2$

The net profit P is given by the model as,

$P=147.8e^{0.196t}$

Where, t represents the year in which $t=4$ corresponds to $2004$.