We are given a table that shows the number of transistors N in 13 different microprocessors, as well as the year they were launched. The year is shown in the left column of the table, while the number of transistors is present in the right column.

Use the model to find the best plot through the points, where t is the year and N is the number of transistors. Keep in mind that is the log's prediction for the number of transistors in the year 1970 and is the model's prediction for the ratio of the increase in the number of transistors every year.

a) Find and that minimize the RMS prediction error, and specify the RMS estimation error (start by taking the log of the number of transistors). Draw a picture that shows the data, as well as the plot line. Use matplotlib.pyplot.scatter to draw the data, matplotlib.pyplot.plt to draw the line, and label the axes on the graph with pyplt.xlabel and pyplt.ylabel. It is required to calculate log₁₀ with numpy.log10 and use numpy.power to find the power.

b) Use the model to predict how many transistors will be in microprocessors that launch in the year 2015. Compare this predictio to the IBM Z13 microprocessor that actually launched in the year 2015 and has approx. 4 x 10⁹ transistors.

c) Compare your results to Moore's law that says that the number of transistors in integrated circuits doubles every one and a half to two years.

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