CPU vs. Transistors
In this project we are going to compare the difference between using a quadratic function and an exponential function to predict the number of transistors in a computer. The table below gives the name of the CPU, the date it was first issued, and the number of transistors in that computer.
Let x = 0 for the year 1971 and have a statistical package or a graphing calculator make a scatterplot with the number of years since 1971 being the independent variable and the number of transistors in a computer x years after 1971 for the dependent variable.
Using a statistical package or a graphing calculator fit a quadratic equation to this data set.
Using this quadratic equation, predict the number of transistors in a computer released for next year and for a computer released in the year 2052.
|
CPU |
Date |
No. of transistors |
|
4004 |
11/15/71 |
2,300 |
|
8008 |
4/72 |
3,500 |
|
8080 |
4/74 |
6,000 |
|
8086 |
6/8/78 |
29,000 |
|
80286 |
2/82 |
134,000 |
|
Intel 386DX |
10/17/85 |
275,000 |
|
Intel 486DX |
4/10/89 |
1,200,000 |
|
Intel DX2 |
3/3/92 |
1,200,000 |
|
Pentium |
3/22/93 |
3,100,000 |
|
Pentium Pro |
11/1/95 |
5,500,000 |
|
Pentium II |
5/7/97 |
7,500,000 |
|
Pentium III |
|
24,000,000 |
|
Pentium IV |
12/00 |
42,000,000 |
CPU vs. Number of transistors
With a statistical package or a graphing calculator fit an equation of the form ln y = . . . .
Rewrite this equation using properties of exponents so it is of the form y = . . . .
Use this equation to predict the number of transistors in a computer released in the next year and for a computer released in the year 2052.
Compare your quadratic predictions with your exponential predictions. Which equation do you think gives the better predictions, the quadratic or exponential? Explain.