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Moore's law. The gure and table below show the number of transistors N in 13 micro- processors, and the year of their introduction. Year 1971 1972 1974 1978 1932 1985 1989 1993 1997 1999 2000 2002 2003 Transistors 2,250 2,500 5.000 20,000 120,000 275,000 1,180,000 3,100,000 7,500,000 24,000,000 42,000,000 220,000,000 410,000,000 Transistors 103 106 10\" 104 103 10" O 00 | | 'I 1970 1975 1980 1985 1990 1995 2000 2005 Year The plot gives the number of transistors on a logarithmic scale. Find the least squares straightline t of the data using the model loglo N z a, + 32(1 ~ 1970), where t is the year and N is the number of transistors. Note that. 61 is the model's prediction of the log of the number of transistors in 1970, and 1092 gives the model's prediction of the fractional increase in number of transistors per year. (a) Find the coeicients 61 and 62 that minimize the EMS error on the data, and give the RMS error on the data. Plot the model you nd along with the data points. (b) Use your model to predict the number of transistors in a microprocessor introduced in 2015. Compare the prediction to the IBM 213 microprocessor, released in 20151 which has around 4 X 109 transistors. {0) Compare your result with Moore's law, which states that the number of transistors per integrated circuit roughly doubles every one and a half to two years