horizontal Asymptote(s) y=?

MATH 133 – Unit 4 Submission Assignment

NAME (Required): _____________________________

Please show all work details with answers, insert the graph, and provide answers to all of the critical thinking questions on this document. Upload this modified Answer Form to the Intellipath Unit 4 Submission lesson. Make sure you submit your work in a modified MS Word document; hand-written work will not be accepted. If you need assistance, please contact your course instructor.

A company wants to study how consumers would rate Internet service providers (ISPs) 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. In the equations, x is the size of files to be downloaded (in megabytes), N(x) is the average ratings in North America (in percent), E(x) is the average ratings in Europe (in percent), and A(x) is the average ratings in Asia (in percent). The consumer ratings can range from 0% (unsatisfactory) to 100% (excellent).

For each question, be sure to show all your work details for full credit. Round all value answers to 3 decimal places.

North America Europe Asia

  1. Based on the first letter of your last name, choose a value for k that you will use in the equations above. It does not necessarily have to be a whole number. Using your chosen value for k, write your version of the three mathematical models here. (10 points)

First Letter of Your Last Name Possible Values For
A–F 100199
G–L 200299
M–R 300399
S–Z 400499

Type your final answers here:
Chosen Value For k
Equation for North America
Equation for Europe
Equation for Asia

  1. Complete the table below by calculating the consumer ratings based on the size of the data. Work must be shown to receive full credit. Show calculation details for and only. (20 points)

Consumer Ratings (in %)

(Round all value answers to 3 decimal places.)

x, size of files

(megabytes)

North America Europe Asia
100
400
900
1,600
2,500

Explain your answer here:

  1. Draw the graphs of the three mathematical models using Excel or another graphing utility. Do this on the same coordinate system so that the functions can be easily compared. (There are free downloadable programs like Graph 4.4.2 or Microsoft’s Mathematics 4.0, online utilities like desmos.com, and many others.) Insert both the function and the graph into the Word document containing your answers and work details. Be sure to label and number the axes appropriately so that the graph matches the chosen and calculated values from above. (20 points)

Insert both your graph and function here:

  1. Using correct function transformation terminology, describe the transformation of the graph of Europe if its parent function is North America. (10 points)

Explain your answer here:

  1. If these functions were considered as functions not representing only values between 0% and 100%, would any of them have horizontal asymptotes? How about vertical asymptotes? If yes, state the asymptote equations. Explain your answers. (20 points)

Equation for North America
Horizontal Asymptote(s) y=?
Vertical Asymptote(s) x=?

Equation for Europe
Horizontal Asymptote(s) y=?
Vertical Asymptote(s) x=?

Equation for Asia
Horizontal Asymptote(s) y=?
Vertical Asymptote(s) x=?

Explain your answer here:

  1. At what size, (in megabytes), will the consumer ratings be equal to 0 in Asia? Show all the work details. (10 points)

Final answer

(Round all value answers to 3 decimal places.)

? megabytes

Explain your answer here:

  1. From both the Internet service providers’ and customers’ perspectives, why do you think it is important to study the consumer ratings of an ISP? Justify your answer. (10 points)

Explain your answer here:

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