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

Question

The annual sales S (in millions of dollars) for the Perrigo Company from 2004 through 2010 are shown in the table. $\begin{array}{cc} Year & 2004 & 2005 & 2006 & 2007 & 2008 & 2009 & 2010 \\ Sales, S & 898.2 & 1024.1 & 1366.8 & 1447.4 & 1822.1 & 2006.9 & 2268.9 \end{array}$

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 $b = e^{\ln b}$ to 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.

Answer 1

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 $f (x) = 488.964 e^{0.158 x}$

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:
$f (11) = 488.964 e^{0.158 (11)} \approx 2768.29$ To predict sales in 2011 using the logarithmic model, find g(11) as follows: $g (11) = - 1333.635 + 1515.088 \ln (11) \approx 2299.39$

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.

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

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