Module Six Discussion Question: Solve the problems below. Copy the description of your Ferris wheel in the text box and include that as part of your initial Discussion post in Brightspace. Using "copy" from here in Mobius and "paste" into Brightspace should work. Hint: This is similar to Question 48 in Section 8.1 of our textbook. We covered this section in "5-1 Reading and Participation Activities: Graphs of the Sine and Cosine Functions" in Module Five. You can check your answers to part a and c to make sure that you are on the right track. A Ferris wheel is 21 meters in diameter and completes 1 full revolution in 16 minutes. A Ferris wheel is 21 meters in diameter and boarded from a platform that is 1 meter above the ground. The six o’clock position on the Ferris wheel is level with the loading platform. The wheel completes 1 full revolution in 16 minutes. The function h (t) gives a person’s height in meters above the ground t minutes after the wheel begins to turn. a. Find the amplitude, midline, and period of h (t) . Enter the exact answers. Amplitude: A = Midline: h = Period: P = Number Number Number meters meters minutes b. Assume that a person has just boarded the Ferris wheel from the platform and that the Ferris wheel starts spinning at time t = 0. Find a formula for the height function h (t) . Hints: What is the value of h (0) ? Is this the maximum value of h (t) , the minimum value of h (t) , or a value between the two? The function sin (t) has a value between its maximum and minimum at t = 0 , so can h (t) be a straight sine function? The function cos (t) has its maximum at t = 0, so can h (t) be a straight cosine function? c. If the Ferris wheel continues to turn, how high off the ground is a person after 60 minutes? Hint Penalty Hint 0.0 View Hint Number Module Three Discussion Question: Solve the problem below. Copy the description of your forecast in the box below and include that as part of your initial Discussion post in Brightspace. Using "copy" from here in Mobius and "paste" into Brightspace should work. Hint: The chart is taken from https://ourworldindata.org/technological-progress (https://ourworldindata.org/technologicalprogress). From the chart, estimate (roughly) the number of transistors per IC in 2018. Using your estimate and Moore's 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 isn't 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. Moore's 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,.1,000 transistors, 10,000 transistors, 100,000 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 (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 ... it's not linear. From the graph, it seems that from 1971 to 1981 the number of transistors went from about 1,000 to 40,000. Moore's Law predicts that in 10 years, it would double 5 times, i.e. go from 1,000 to 32,000, 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 4,000 (a rough estimate by eye). Using this estimate and Moore's Law, what would you predict the number of transistors per IC to be 20 years later, in 1992? Prediction = Number Part b: From the chart, estimate (roughly) the number of transistors per IC in 2018. Using your estimate and Moore's 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?
Purchase answer to see full attachment