Gordon Moore, one of the founders of Intel Corporation, predicted in 1965 that the number of transistors on an integrated
circuit would double every 18 months. This is “Moore’s law,” one way to measure the revolution computing. Here are data
on the dates and number of transistors for Intel microprocessors:
Processor
4004
8008
8080
8086
286
386
486D
Pentium
Pentium II
Pentium III
Pentium 4
Date
1971
1972
1974
1978
1982
1985
1989
1993
1997
1999
2000
Transistors
2250
2500
5000
29000
120000
275000
1180000
3100000
7500000
24000000
42000000
1)
Draw a scatterplot of this data. The x-axis is the date and the y-axis is the number of transistors. Describe the shape
of the scatterplot. This shape indicates the data is not a linear fit.
2)
Use technology to find the least squares regression line of the data. Record the equation and the correlation.
3)
Draw a scatterplot of the years (x axis) versus the residuals (y axis). Describe the shape of the scatterplot. This shape
indicates the data is not a linear fit, but has a pattern.
4)
In a chart record the x values (years) and the natural log (ln) of the y values (transistors). Draw a scatter plot of the
years (x-axis) versus the natural ln of y values (y axis). This shape indicates the data is now a linear fit.
5)
Use technology to find the least squares regression line. That is ln (y)=….
6)
Rewrite your equation from 6) as a y= e^(…. equation.
7)
Use the equation from 7) to predict the number of transistors in 2005 and 2010. Use google to comment on your
answer.
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2 marks