The power of personal computers has increased dramatically as a result of the ability to place an increasing number of transistors on a single processor chip. The following table lists the number of transistors on some popular computer chips made by Intel.

a. Let t be the year, where t = 0 corresponds to 1985, and y be the number of transistors (in millions). Find functions of the form y = mt + b, y = at² + b  and y = ab^t that fit the data at 1985 and 2009.

b. Use a graphing calculator to plot the data in the table and to graph the three functions found in part a. Which function best fits the data?

c. Use the best-fitting function from part b to predict the number of transistors on a chip in the year 2015.

d. If you have a graphing calculator or computer program with an exponential regression feature, use it to find an exponential function that approximately fits the data. How does this answer compare with the answer to part b?

e. In 1965 Gordon Moore wrote a paper predicting how the power of computer chips would grow in the future. Moore’s law says that the number of transistors that can be put on a chip doubles roughly every 18 months. Discuss the extent to which the data in this exercise confirms or refutes Moore’s law.

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Year 1985 1989 1993 1997 1999 2000 2005 2007 2009 Chip 386 486 Pentium Pentium II Pentium III Pentium 4 Pentium D Penryn Nehalem Transistors (in millions) 0.275 1.2 3.1 7.5 9.5 42 291 820 1900