The annual sales S (in millions of dollars) for the Perrigo Company from 2004 through 2010 are shown in the table.begin{array}{|c|c|} hline text{Year} & 2004 & 2005 & 2006 & 2007 & 2008 & 2009 & 2010

alesterp 2021-01-19 Answered

The annual sales S (in millions of dollars) for the Perrigo Company from 2004 through 2010 are shown in the table. Year2004200520062007200820092010Sales, S898.21024.11366.81447.41822.12006.92268.9

a) Use a graphing utility to create a scatter plot of the data. Let t represent the year, with t=4 corresponding to 2004. b) Use the regression feature of the graphing utility to find an exponential model for the data. Use the Inverse Property b=eln bto rewrite the model as an exponential model in base e. c) Use the regression feature of the graphing utility to find a logarithmic model for the data. d) Use the exponential model in base e and the logarithmic model to predict sales in 2011. It is projected that sales in 2011 will be $2740 million. Do the predictions from the two models agree with this projection? Explain.

 

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Expert Answer

Alara Mccarthy
Answered 2021-01-20 Author has 85 answers

Step 1 Exponential Regression Model Step 2

a) A scatter plot of the given data is displayed below:

Step 3

b) Using the regression feature, we find that an exponential model for the data in base e is f(x)=488.964e0.158x


Step 4

c) Using the regression feature, A logarithmic model of given data is given by
g(x)= 1333.635 + 1515.088 ln (x)

 

Step 5

d) To predict sales in 2011 using the exponential model, find f(11) as follows:
f(11)=488.964e0.158(11)  2768.29 To predict sales in 2011 using the logarithmic model, find g(11) as follows: g(11)= 1333.635 + 1515.088 ln (11)  2299.39

 The exponential model closely agrees with the projected amount. The exponential model is only off by about 28.29 million while the logarithmic model is off by a significant 440 million.

 

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