MATH233 Unit 3 Individual ProjectNAME (Required): _____________________________This assignment features an exponential function that is closely related to Moore’s Law, which states that the numbers of transistors per square inch in Central Processing Unit (CPU) chips will double every 2 years. This law was named after Dr. Gordon Moore.Table 1 below shows selected CPUs from this leading processor company introduced between the years 1982 and 2008 in relation to their corresponding processor speeds of Million Instructions per Second (MIPS).Table 1: Selected CPUs with corresponding speed ratings in MIPS. Processor Year t Years After 1982 When Introduced Million Instructions per Second (MIPS) 4 1982 0 1.28 5 1985 3 2.15 6 1989 7 8.7 7 1992 10 25.6 8 1994 12 188 9 1996 14 541 10 1999 17 2,064 11 2003 21 9,726 12 2006 24 27,079 13 2008 26 59,455 (Instructions per second, n.d.)This information can be mathematically modeled by the exponential function:MIPS(t) = (0.112)(1.405^(1.14t+9.12))NOTE: This function is created as a “best fit” function for a table of empirical data and, therefore, does not exactly match many (or any) of the data values in the table above.Rather, the total cumulative differences from all of the data points is at a minimum for this function.Be sure to show your work details for all calculations and explain in detail how the answers were determined for critical thinking questions. Round all value answers to three decimals.1.Generate a graph of this function, MIPS(t) = (0.112)(1.405^(1.14t+9.12)), years after 1982, using Excel or another graphing utility. (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 your Word document that contains all of your work details and answers. Be sure to label and number the axes appropriately. (Note: Some graphing utilities require that the independent variable must be “x” instead of “t”.)2.Find the derivative of with respect to .Show your work details.3.Choose a -value between 10 and 26. Calculate the value of Show your work details.4.Interpret the meaning of the derivative value that you just calculated from part 3 in terms of the function and this scenario.5.If the function is reasonably accurate, for what value of will the rate of increase in MIPS per year reach 6,000,000 ? Approximately which year does that correspond to?Show your work details.6.For the -value you chose in part 3 above, find the equation of the tangent line to the graph of at that value of . What information about the function can be obtained from the tangent line? Show your work details.7.Using Web or Library resources research to find the years of introduction and the processor speeds for both the CPU A and the CPU B. Be sure to cite your creditable resources for these answers. Convert the years introduced to correct values of by subtracting 1982 from each year.Then, determine how well the function predicts the forecast CPUs’ processor speeds by comparing the calculated values with the actual MIPS ratings of these two CPUs. Show your work details.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/ Instructions per second. (n.d.). Wikipedia.Retrieved from http://en.wikipedia.org/wiki/Instructions_per_seco…Intel. (2008). Mircoprocessor quick reference guide. Retrieved from http://www.intel.com/pressroom/kits/quickrefyr.htm Laird, J. (2011, January 3). Intel Core i5-2500K review. Techradar. Retrieved from http://www.techradar.com/us/reviews/pc-mac/pc-comp… Laird, J. (2013, June 3). Intel Core i7-4770K review. Techradar. Retrieved from http://www.techradar.com/us/reviews/pc-mac/pc-comp… Mathematics 4.0. (n.d.). Retrieved from the Microsoft Web site: http://microsoft-mathematics.en.uptodown.com/MATH233 Unit 3 Individual Project

NAME (Required): _____________________________

This assignment features an exponential function that is closely related to Moore’s Law, which

states that the numbers of transistors per square inch in Central Processing Unit (CPU) chips will

double every 2 years. This law was named after Dr. Gordon Moore.

Table 1 below shows selected CPUs from this leading processor company introduced between

the years 1982 and 2008 in relation to their corresponding processor speeds of Million

Instructions per Second (MIPS).

Table 1: Selected CPUs with corresponding speed ratings in MIPS.

Processor

Year

t Years After 1982

When Introduced

Million Instructions

per Second (MIPS)

4

5

6

7

8

9

10

11

12

13

1982

1985

1989

1992

1994

1996

1999

2003

2006

2008

0

3

7

10

12

14

17

21

24

26

1.28

2.15

8.7

25.6

188

541

2,064

9,726

27,079

59,455

(Instructions per second, n.d.)

This information can be mathematically modeled by the exponential function:

MIPS(t) = (0.112)(1.405^(1.14t+9.12))

NOTE: This function is created as a “best fit” function for a table of empirical data and,

therefore, does not exactly match many (or any) of the data values in the table above. Rather, the

total cumulative differences from all of the data points is at a minimum for this function.

Be sure to show your work details for all calculations and explain in detail how the answers

were determined for critical thinking questions. Round all value answers to three decimals.

1. Generate a graph of this function, MIPS(t) = (0.112)(1.405^(1.14t+9.12)), years after

1982, using Excel or another graphing utility. (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 your Word document that contains all of your work

Page 1 of 3

details and answers. Be sure to label and number the axes appropriately. (Note: Some

graphing utilities require that the independent variable must be “x” instead of “t”.)

2. Find the derivative of ( ) with respect to . Show your work details.

3. Choose a -value between 10 and 26. Calculate the value of ′( ). Show your work

details.

4. Interpret the meaning of the derivative value that you just calculated from part 3 in terms

of the ( ) function and this scenario.

5. If the ( ) function is reasonably accurate, for what value of will the rate of

increase in MIPS per year reach 6,000,000 ? Approximately which year does that

correspond to? Show your work details.

6. For the -value you chose in part 3 above, find the equation of the tangent line to the

graph of ( ) at that value of . What information about the ( ) function can

be obtained from the tangent line? Show your work details.

7. Using Web or Library resources research to find the years of introduction and the

processor speeds for both the CPU A and the CPU B. Be sure to cite your creditable

resources for these answers. Convert the years introduced to correct values of by

subtracting 1982 from each year. Then, determine how well the ( ) function

predicts the forecast CPUs’ processor speeds by comparing the calculated values with the

actual MIPS ratings of these two CPUs. Show your work details.

References

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

Page 2 of 3

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

Instructions per second. (n.d.). Wikipedia. Retrieved from

http://en.wikipedia.org/wiki/Instructions_per_second

Intel. (2008). Mircoprocessor quick reference guide. Retrieved from

http://www.intel.com/pressroom/kits/quickrefyr.htm

Laird, J. (2011, January 3). Intel Core i5-2500K review. Techradar. Retrieved from

http://www.techradar.com/us/reviews/pc-mac/pc-components/processors/intel-core-i52500k-917570/review

Laird, J. (2013, June 3). Intel Core i7-4770K review. Techradar. Retrieved from

http://www.techradar.com/us/reviews/pc-mac/pc-components/processors/intel-core-i74770k-1156062/review

Mathematics 4.0. (n.d.). Retrieved from the Microsoft Web site: http://microsoftmathematics.en.uptodown.com/

Page 3 of 3

Purchase answer to see full

attachment

#### Why Choose Us

- 100% non-plagiarized Papers
- 24/7 /365 Service Available
- Affordable Prices
- Any Paper, Urgency, and Subject
- Will complete your papers in 6 hours
- On-time Delivery
- Money-back and Privacy guarantees
- Unlimited Amendments upon request
- Satisfaction guarantee

#### How it Works

- Click on the “Place Order” tab at the top menu or “Order Now” icon at the bottom and a new page will appear with an order form to be filled.
- Fill in your paper’s requirements in the "
**PAPER DETAILS**" section. - Fill in your paper’s academic level, deadline, and the required number of pages from the drop-down menus.
- Click “
**CREATE ACCOUNT & SIGN IN**” to enter your registration details and get an account with us for record-keeping and then, click on “PROCEED TO CHECKOUT” at the bottom of the page. - From there, the payment sections will show, follow the guided payment process and your order will be available for our writing team to work on it.