MATH133 AIU Solve Equations Mathematical Models Questions

MATH133 – Unit 4 Point-values:Question
Point-value
1
20
2
20
3
20
4
20
5
20
Total
100
You earned
Comments
MATH 133 – Unit 4 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:
Your company studied how consumers would rate Internet service providers based on the size
of files that they download (x). The following equations model the relationship between two
variables from the result of a survey conducted in North America, Europe, and Asia:
North America
𝑁(𝑥) =
𝑘
√𝑥
Europe
𝐸(𝑥) =
𝑘
√𝑥
Asia
+5
𝐴(𝑥) =
𝑘
√𝑥
−7
In these equations, you have the following variables:
• x is the size of files to be downloaded (in megabytes).
• k is the speed of download.
• N(x) is the average ratings in North America (in percent).
• E(x) is the average ratings in Europe (in percent).
• A(x) is the average ratings in Asia (in percent).
The consumer ratings can range from 0% (unsatisfactory) to 100% (excellent).
Page 1 of 4
1. From the table below, use the row that matches the first letter of your last name to select
a value for k that you will use in the equations above. It does not necessarily have to be a
whole number.
First Letter of Your Last Name
Possible Values for 𝒌
A–F
G–L
M–R
S–Z
100–199
200–299
300–399
400–499
Using your chosen value for k, write your version of the three mathematical models below.
(20 points)
Chosen Value for k
Equation for North America
N(x)
Equation for Europe
E(x)
Equation for Asia
A(x)
2. Complete the table below by calculating the consumer ratings using the equations from
Problem 1 for North America, Europe, and Asia and using the values of x below.
Show your calculation details for 𝑥 = 100. (20 points)
Consumer Ratings (in %)
(Round value answers to 3 decimal places.)
x, Size of Files
(in Megabytes)
100
North America
Europe
Asia
400
900
1,600
2,500
Page 2 of 4
Show your work for x = 100 here:
3. Draw the graphs of the three equations from Problem 1 using desmos.com, Excel, or any
similar online utilities. Label each equation shown as a different color, and put all of these
on the same graph. An introduction to desmos.com can be found at
http://learn.desmos.com/graphing.
Be sure to title the graph as your first and last name. In addition, label and number the xaxis and the y-axis appropriately so that the graph matches the calculated values from
above. Use the axes scales of 0 ≤ 𝑥 ≤ 2,500 and −10 ≤ 𝑦 ≤ 30. (20 points)
Insert your graph here:
4. Using correct function transformation terminology, describe the transformation of the
graph of Europe [E(x)] if its parent function is North America [N(x)]. (20 points)
Page 3 of 4
5. Let
𝐴(𝑥) =
100
√𝑥
−7
At what value of x (in megabytes) will A(x) = 0? Show all of your work details. (20 points)
Value of x in megabytes
(Round value answers to 3 decimal
places.)
Show your work here:
Page 4 of 4