Profit The net profits P (in millions of dollars) of Express Scripts from 2004 through 2013 are shown in the table.

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

Spreadsheet at Larson Applied Calculus.com

A model for these data is given by P =   147.8 e 0. l 96 t , where t represents the year, with t = 4 corresponding to 2004. (Source: Express Scripts Holding Co.)

(a) How well does the model fit the data?

(b) Find a linear model for the data. How well does the linear model fit the data? Which model, exponential or linear, is a better fit?

(c) Use both models to predict the net profit in 2018.

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:

The net profit P is given by the model as,

P=147.8e0.196t

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

Given information:

The table representing the net profits P (in millions of dollars) earned by Express Scripts during the period 2004−2013 is as follows:

The net profit P is given by the model as,

P=147.8e0.196t

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

Consider the model, P=147.8e0.196t

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

Compute the profit in 2004 by substituting t=4 in the model as,

P(4)=147.8e0.196(4)=147.8e0.784≈147.8⋅2.190216≈$323.7 million

Compute the profit in 2005 by substituting t=5 in the model as,

P(5)=147.8e0.196(5)=147.8e0.98≈147.8⋅2.664456≈$393.8 million

Compute the profit in 2006 by substituting t=6 in the model as,

P(6)=147.8e0.196(6)=147.8e1.176≈147.8⋅3.241383≈$479.1 million

Compute the profit in 2007 by substituting t=7 in the model as,

P(7)=147.8e0.196(7)=147.8e1.372≈147.8⋅3.94323≈$582

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:

The net profit P is given by the model as,

P=147.8e0.196t

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

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:

The net profit P is given by the model as,

P=147.8e0.196t

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