MATH 133 AIU Calculate the Corresponding Values of Function Algebra Questions

MATH133 – Unit 3 Point-values:Question
Point-value
1
20
2
20
3
20
4
20
5
20
Total
100
You earned
Comments
MATH133 – Unit 3 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 or desmos.com (or
other graph program) as described in the Unit 1 Discussion Board.
3. Provide final answers to all questions in boxes provided.
4. Round all value answers to 3 decimal places, unless otherwise noted.
Formulas Provided:
A simplified speedup function for using multiple parallel processors can be calculated
approximately using the following rational equation:
𝑆(𝑥) =
𝑥
𝑝𝑥 + (1 − 𝑝)
where 𝑥 is the number of processors used, and 𝑝 is the decimal equivalent of the percent of the
program that must be run sequentially.
The following is a link to help you understand how parallel processing works:
https://computer.howstuffworks.com/parallel-processing.htm
1. From the table below, use the row that matches the first letter of your last name to
select a percent of a program that must be run sequentially:
First Letter of Your Last Name
A–F
G–L
M–R
Possible Values for 𝒑
(Maximum of 3
Decimals)
9.5–12.49%
12.5–15.49%
15.5–18.49%
Page 1 of 5
S–Z
18.5−21.49%
Using the decimal equivalent for your chosen value of 𝑝, write your version of the
simplified speedup function, 𝑆(𝑥), below. (20 points)
Chosen Value of p
(in Decimal Form)
Simplified Speedup
Function, S(x)
2. Using the simplified speedup function that you submitted in Question 1, complete the
table below.
Calculate the corresponding values of function 𝑆(𝑥) for each 𝑥 value. To receive full
credit, show all of your calculation details for x = 20. (20 points)
Chosen 𝒙 Values
Calculated 𝑺(𝒙) Values
(Round to 3 Decimal Places)
10
20
30
80
90
100
Show your work here for the x value of 20:
3. Use desmos.com, Excel, or any similar online utilities to graph the speedup function. An
introduction to desmos.com can be found at http://learn.desmos.com/graphing.
Page 2 of 5
Be sure to title the graph as your first and last name. In addition, label and number the
x-axis and the y-axis appropriately so that the graph follows from above, showing the
domain for 0 ≤ 𝑥 ≤ 100. (20 points)
Insert your graph here:
4. Parallel processing uses two or more computers working to together to solve a problem.
Parallel processing efficiency depends on the program. A single processor must
complete certain parts of the program while the other processors wait for results. This
creates some bottlenecks, which are represented by a percentage of the program that
must operate sequentially. If Computer A can solve the problem in 8 hours, Computer B
can solve the problem in 6 hours, and the required sequential operation of the program
is 20%, how many hours would it take both computers working together in parallel
processing to solve the problem? (20 points)
Hint: Since 20% of the program requires one computer to work alone, you will use the
faster computer, Computer B, to work on that part of the program; then, you will use both
computers to complete the remaining 80% of the program.
Page 3 of 5
How many hours?
(Round all value answers to 3 decimal
places.)
Show your work here:
5. Working together in parallel processing, two computers can complete a task in C hours.
Computer X working alone can complete the task in 3 hours less than Computer Y. One
hundred percent of the task needs to be completed. Portion P of the task must be done
by Computer X, and portion 1 – P must be done by Computer Y. How long does it take
each computer to complete the task alone? From the table below, select values for C
and P according to the first letter of your last name. (20 points)
First Letter of Your Last Name
A–F
G–L
M–R
S–Z
Possible Values for C
(Maximum of 1
Decimal)
2–3
4–5
6–7
8–9
Possible Values for P
(Maximum of 2
Decimals)
0.1–0.2
0.2–0.3
0.3–0.4
0.4–0.5
Time it takes Computer X to
complete the task
(Round all value answers to 3
decimal places.)
Page 4 of 5
Time it takes Computer Y to
complete the task
(Round all value answers to 3
decimal places.)
Show your work here:
Page 5 of 5