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

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