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MATH 133 Unit 4 Individual Project

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MATH 133 Unit 4 Individual Project

Please show all work details with answers, insert the graphs, and provide answers
to all the critical thinking questions on this form for the Unit 4 IP assignment.
A company wants to study how consumers would rate Internet service providers (ISP’s)
based on the size of files that they download. 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 three decimal places.
North America N (x )= Europe k
√x E ( x )= Asia k
+5
√x A ( x) = k
−10
√x 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.
First letter of your last name Possible values for k A–F 500–599 G–L 600–699 M–R 700–799 S–Z 800–899 2. Using your chosen value for k, write your version of the three mathematical models.
3. Complete the table below by calculating the consumer ratings based on the size of the
data. Work must be shown to receive full credit. Consumer Ratings (in %)
x, size of files North America Europe Asia Page 1 of 2 100
400
900
1,600
2,500
4. Using Excel or another graphing utility (There are free downloadable programs like
Graph 4.4.2 or Mathematics 4.0; or, there are also online utilities such as this site and
many others.), draw the graphs of the three mathematical models on the same
coordinate system so that the functions can be easily compared.
5. Describe the transformation of the graph of Europe with North America.
6. Describe the transformation of the graph of Asia with North America.
7. Do the graphs have horizontal asymptotes? How about vertical asymptotes? Explain
your answers.
8. At what size, x (in megabytes), will the consumer ratings be equal to 0 in Asia?
9. Why do you think is it important to study the consumer ratings of an Internet service
provider (ISP)? Explain your answer.
References
Desmos. (n.d.). Retrieved from https://www.desmos.com/
Graph 4.4.2. (n.d.). Retrieved from the Graph Web site: http://www.padowan.dk/
Mathematics 4.0. (n.d.). Retrieved from the Microsoft Web site:
https://www.microsoft.com/en-us/default.aspx Page 2 of 2