Intel processors transistor count from 1971 to present table

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MATH133: Unit 5 Individual Project

In this assignment you will study an exponential function that is similar to Moore’s Law that

was formulated by Dr. Gordon Moore, cofounder and Chairman Emeritus of Intel

Corporation.

The following is a table representing the number of transistors in Intel CPU chips between

the years 1971 and 2000:

Processor Transistor Count Year of Introduction

Intel 4004 2,300 1971

Intel 8085 6,500 1976

Intel 80286 134,000 1982

Intel 80486 1,180,235 1989

Pentium Pro 5,500,000 1995

Pentium 4 42,000,000 2000

Core 2 Duo ? 2006

Core 2 Duo and Quad Core +

GPU Core i7

? 2011

If x equals the number of years after 1971 (the year 1971 means x = 0), then these data

can be mathematically modeled by the exponential function y = f(x) = 2,300(1.4x).

For each question, be sure to show all your work details for full credit. Round all

value answers to three decimal places.

1. Graph your function using Excel or another graphing utility. (For the graph to show

up in the viewing window, use the x-axis scale of [-10, 40], and for the y-axis scale,

use [-10,000,000, 50,000,000]). (There are free downloadable programs like Graph

4.4.2 or Mathematics 4.0; or, there are also online utilities such as this site and

many others.) Insert the graph into the supplied Student Answer Form. Be sure to

label and number the axes appropriately so that the graph matches the chosen and

calculated values from above.

2. Based on this function, what would be the predicted transistor count for the years

2006 and 2011? Show all the work details.

3. Using the library or Internet resources, find the actual transistor count in the years

2006 and 2011 for Intel’s Core 2 Duo and Quad Core + GPU Core i7, respectively.

Compare these values to the values predicted by the function in part 2 above. Are

the actual values over or under the predicted values and by how much? Explain what

this information means in terms of the mathematical model function y = f(x) =

2,300(1.4x). Be sure to reference your source(s).

4. Examine the connection between the exponential and logarithmic forms to your

problem. First, for y = bx if and only if x = logby, both equations give the exact same

relationship among x, y, and b. Next, use the rule of logarithms log𝑏 𝑀

𝑁 = log𝑏𝑀 −

http://www.padowan.dk/

http://www.padowan.dk/

https://www.microsoft.com/en-us/default.aspx

https://www.desmos.com/

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log𝑏 𝑁. Applying the given relations, convert the function y = f(x) = 2,300(1.4 x) into

logarithmic form.

5. Then, examine the function y = g(x) = log1.4(x) – log1.42,300. Discuss and

demonstrate the relationship between the functions y = f(x) and y = g(x).

6. In the mathematical model function y = f(x) = 2,300(1.4x), replace 2,300 with a

chosen number between 1,390 and 1,960. (For example, y = f(x) = 1,400(1.4x) uses

1,400 for the chosen value). How well does this new mathematical model match the

given data in the table above? What does this tell you about the mathematical model

function y = f(x) = 2,300(1.4x)?

References

Desmos. (n.d.). Retrieved from https://www.desmos.com/

Graph 4.4.2. (n.d.). Retrieved from the Graph Web site: http://www.padowan.dk/

Mathematics 4.0. (n.d.). Retrieved from the Microsoft Web site:

https://www.microsoft.com/en-us/default.aspx

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