MATH 133 AIU Exponential Function Depreciation Model Worksheet

you just have to fill the work sheet out First name Rachael last Name Campbell

MATH133-Unit 5 Point-values:
Question
Point-value
1
20
2
20
3
20
4
20
5
20
Total
100
You earned
Comments
MATH133 – Unit 5 Individual Project
NAME (Required): ___________________
Assignment Instructions:
1. For each question, show all of your work for full credit.
2. Insert all labeled and titled graphs by using screenshots from Excel, desmos.com, or
other graphing programs as described in the Unit 1 Discussion Board.
3. Provide the final answers to all of the questions in the boxes provided.
4. Round off all answers to 3 decimal places unless otherwise noted.
In this assignment, you will study an exponential function that is similar to Moore’s law.
The following table presents the actual number of transistors for Premium central processing
unit (CPU) chips between 1971 and 2017:
Processor
Premium Processor 1
Premium Processor 2
Premium Processor 3
Premium Processor 4
Premium Processor 5
Premium Processor 6
Premium Processor 7
Premium Processor 8
Transistor Count
2,200
7,400
133,400
1,175,000
2,409,000
41,099,000
290,909,000
17,905,000,000
Year of Introduction
1971
1976
1982
1989
1995
2000
2006
2017
If you let 𝑥 be the number of years after 1971 (i.e., the year 1971 means 𝑥 = 0), then these
data can be mathematically modeled by the following exponential function:
𝒚 = 𝒇(𝒙) = 𝟏, 𝟖𝟐𝟐. 𝟖 × (𝟏. 𝟒𝒙 )
1. Use desmos.com, Excel, or any similar online utilities to graph the following function:
Page 1 of 6
𝑦 = 1,822.8 × 1.4𝑥
An introduction to desmos.com can be found at http://learn.desmos.com/graphing.
Be sure to title the graph with your first and last name. Also, label and number the x-axis
and y-axis appropriately so that the graph matches the chosen and calculated values
from the data above. Use axes scales of -10 < x < 20 and -10,000 < y < 200,000 for the graph to show up properly in the viewing window. (20 points) Insert your graph below: 2. Based on the function Page 2 of 6 3. 𝑦 = 𝑓(𝑥) = 1,822.8 × (1.4𝑥 ) what would be the predicted transistor count for the years 2006 and 2017? Do not forget that x is the number of years after 1971, so for 1971, x = 0. Show all of the calculation details. (20 points) Transistor Count for 2006 Round off the final answer to the nearest whole value. Transistor Count for 2017 Round off the final answer to the nearest whole value. Show your work below: Page 3 of 6 3. Calculate the value of 𝑥 where the function 𝑦 = 𝑓(𝑥) = 1,822.8 × (1.4𝑥 ) will predict the transistor value 𝑓(𝑥) = 406,500,000,000. (20 points) Final answer (x) Round off the final answer to the nearest whole value. Exact year Show your work below: Page 4 of 6 Value Depreciation Model 4. A company purchases a complete industrial networking system for $32,145. The value of the system depreciates at a rate of 7.5% per year. How much will it be worth in 5.5 years, and how long will it take until the system is worth $10,000? (20 points) How much will it be worth in 5.5 years? Round off the answer to 2 decimal places. For what value of x will the system be worth $10,000? Round off the answer to 2 decimal places. Show your work below: Page 5 of 6 Smithville Manufacturing Employee Model 5. Information technology (IT) administrators must plan for the future computing needs of organizations, which are often based on the number of employees. Let y be the number of employees at Smithville Manufacturing. The number of employees is increasing according to the mathematical model 𝑦 = 1,600(1.25)𝑥 where x is the number of years. Solve the problems in the following table. Place your answers in the table, and show your work below the table. (20 points) What is the starting number of employees for Smithville Manufacturing? Round off the final answer to the nearest whole value. What would the number of employees be in 10 years if this trend continues? Round off the final answer to the nearest whole value. Use this model to predict the number of years (x) that Smithville Manufacturing will have 5,000 employees. Round off the final answer to the nearest one decimal place. Show your work below: Page 6 of 6