12.56 Moore’s law today The following data show the number of components (per square inch, in millions) being packed on a Pentium-type chip, for years 1994 to 2015.

Let x be the number of years since 1994 (e.g., x = 0 for 1994, x = 3 for 1997, …, x = 21 for 2015) and let y be the number of components on a chip. The prediction equation when fitting an exponential regression model to these data equals yn = 151.61 * 1.191x.

a. What is the predicted number of components per square inch in 2015?

b. By how much does the predicted number of components increase per year over the time range that these data cover?

c. The correlation between the logarithm of the count and x equals 0.985, and the scatterplot with the log counts shows a linear trend. What does this suggest about whether the exponential regression model is appropriate for these data?

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Chip Pentium Year Count Chip Year Count 1994 14 PentiumE 2008 1794 PentiumII 1997 24 PentiumG 2010 3043 PentiumIII 1999 48 PentiumG 2011 2482 Pentium4 2000 125 PentiumG 2013 5645 PentiumD 2005 720 PentiumG 2015 5103 PentiumE 2007 971