Assignment
Please show all work details with answers, insert the graphs, and provide answers to all the critical thinking questions on this form for the 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.
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North America
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Europe
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Asia
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N(x)=k/√x
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E(x)=k/√x+5 |
A(x)=k/√x-10 |
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.
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First letter of your last name
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Possible values for k
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A-F
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500-599
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G-L
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600-699
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M-R
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700-799
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S-Z
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800-899
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Using your chosen value for k, write your version of the three mathematical models.
Complete the table below by calculating the consumer ratings based on the size of the data. Work must be shown to receive full credit.
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Consumer Ratings (in %)
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x, size of files
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North America
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Europe
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Asia
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100
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400
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900
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1,600
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2,500
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Using Excel or another graphing utility, draw the graphs of the three mathematical models on the same coordinate system so that the functions can be easily compared.
Describe the transformation of the graph of Europe with North America.
Describe the transformation of the graph of Asia with North America.
Do the graphs have horizontal asymptotes? How about vertical asymptotes? Explain your answers.
At what size, x(in megabytes), will the consumerratings be equal to 0 in Asia?
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