Gordon Moore, one of the founders of Intel Corporation, predicted in 1965 that t

Question

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," and offers one way to measure the revolution in computing. This Excel fileprovides data on the dates and number of transistors for Intel micrprocessors.

Question 1. Subtract 1971 from all the dates so that 1971 becomes year 0, 1972 becomes year 1, and so on. Make a scatterplot of the data with transistors on the y-axis and date on the x-axis. From the scatterplots shown below select the scatterplot that most closely resembles your scatterplot. Indicate your answer by placing the letter of the plot in the answer box.
Plot

Question 2. Suppose that Moore's law is correct and the number of transistors is 2,250 in year 0 (1971) and doubles every 18 months (1.5 years). What mathematical model should be used for predicting transistors in year x after 1971?

y = 2250 + 2xy = 2250 + x1.5    y = 2250 * x2y = 2250 * x1.5y = 2250*2x/1.5y = 2250x + x2

Question 3. What transformation on the y-variable should be used to create a better linear fit between x (year) and the transformed y?

log10(y)    

10y

Question 4. Using the transformation on the y-variable from Question 3, determine the least squares line between x (year) and the transformed y. Enter the slope and intecept below (use 3 decimal places).

slope
intercept

Question 5. Use the least squares line in question 3 to predict the number of transistors on a chip in 2012.

transistors

Question 6. While transistor counts have grown exponentially, they have grown a bit more slowly than Moore's law predicts. Let's quickly see why. According to your model in question 2, what is the slope of the line that connects the logarithm of transistors with the explanatory variable year? Enter the slope in the answer box below. Compare this slope with the slope of the least squares prediction line in question 4.

slope of line from mathematical model

The data:

Explanation / Answer

Q1) plot A

Q2)

y = 2250 + 2x

Q4)

slope = 2

intercept = 2250

Related Questions

Navigate

• Browse (All)
• Browse G
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.