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MATH 133 How do I graph f(35) and f(40)

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MATH 133 How do I graph f(35) and f(40)

MATH 133 How do I graph f(35) and f(40)

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
Intel 4004
Intel 8085
Intel 80286
Intel 80486
Pentium Pro
Pentium 4
Core 2 Duo
Core 2 Duo and Quad Core +
GPU Core i7 Transistor Count
2,300
6,500
134,000
1,180,235
5,500,000
42,000,000
?
? Year of Introduction
1971
1976
1982
1989
1995
2000
2006
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 log = log − Page 1 of 2 log . Applying the given relations, convert the function y = f(x) = 2,300(1.4x) 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.)