The speed of a computer has increased with time in a consistent way. In 1965, Dr. Gordon Moore (b 1929), a co-founder of Intel, noted that the number of transistors per square inch on integrated circuits seems to double approximately every 18 months. The table below shows the year of introduction of a new chip and the number of transistors on that chip.
Year of introduction x Number of transistors y
1971 ...................................... 2,250
1972 ...................................... 2,500
1974 ...................................... 5,000
1978 .................................... 29,000
1982 .................................. 120,000
1985 .................................. 275,000
1989 ................................ 1,180,000
1993 ................................ 3,100,000
1997 ............................... 7,500,000
1999 .............................. 24,000,000
2000 .............................. 42,000,000
a. Make a scatter plot of the data. (Let x = 0 represent 1970.) Is the data linear?
b. Make a scatter plot of (log x, y), (x, log y), and (log x, log y). Which is most linear?
c. Find a least squares line to model the most linear data you found in 8b.
d. Using the least squares line in 8c, write an equation to model the data.
e. Use your model to make a prediction about the number of transistors on a microchip in 2011.