Week 3 Exponential Models

Hint: The chart is taken from https://ourworldindata.org/technological-progress. From the chart estimate (roughly) the number of transistors per IC in 2012. Using your estimate and Moores Law what would you predict the number of transistors per IC to be in 2040? In some applications the variable being studied increases so quickly (“exponentially”) that a regular graph isnt informative. There a regular graph would show data close to 0 and then a sudden spike at the very end. Instead for these applications we often use logarithmic scales. We replace the y-axis tick marks of 1 2 3 4 etc. with y-axis tick marks of 101 = 10 102 = 100 103 = 1000 104 = 10000 etc. In other words the logarithms of the new tick marks are equally spaced. Technology is one area where progress is extraordinarily rapid. Moores Law states that the progress of technology (measured in different ways) doubles every 2 years. A common example counts the number of transitors per integrated circuit. A regular y-axis scale is appropriate when a trend is linear i.e. 100 transistors 200 transistors 300 transistors 400 transistors etc. However technology actually increased at a much quicker pace such as 100 transistors.1000 transistors 10000 transistors 100000 transistors etc. The following is a plot of the number of transistors per integrated circuit over the period 1971 – 2008 taken from https://ourworldindata.org/technological-progress (that site contains a lot of data not just for technology). At first this graph seems to show a steady progression until you look carefully at the y-axis … its not linear. From the graph it seems that from 1971 to 1981 the number of transistors went from about 1000 to 40000. Moores Law predicts that in 10 years it would double 5 times i.e. go from 1000 to 32000 and the actual values (using very rough estimates) seem to support this. The following is the same plot but with the common logarithm of the y-axis shown. You can see that log(y) goes up uniformly. Questions to be answered in your Brightspace Discussion: Part a: The number of transistors per IC in 1972 seems to be about 4000 (a rough estimate by eye). Using this estimate and Moores Law what would you predict the number of transistors per IC to be 20 years later in 1992? Prediction = Part b: From the chart estimate (roughly) the number of transistors per IC in 2012. Using your estimate and Moores Law what would you predict the number of transistors per IC to be in 2040? Part c: Do you think that your prediction in Part b is believable? Why or why not? This is all the material that you will need. Please let me know if you have any questions. Requirements: a detail explanation with how you came with an answer | .doc file