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Intel processors transistor count from 1971 to present table

21/12/2020 Client: saad24vbs Deadline: 6 Hours

Page 1 of 2


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/

Page 2 of 2


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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