MATH 133 - Unit 4 Individual Project NAME (Required): __________Aliya Abdi___________________ Please show all work details with answers, insert the graph, and provide answers to all of the critical thinking questions on this document. 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 +1 x E ( x )= Asia k +10 x A ( x) = k 12 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. Using your chosen value for k, write your version of the three mathematical models here. First letter of your last name Possible values for A-F 500 - 599 G-L 600 - 699 M-R 700 - 799 S-Z 800 - 899 k Page 1 of 3 2. 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 x=900 and x=1600 only. Consumer Ratings (in %) x, size of files North America Europe Asia 100 400 900 1,600 2,500 3. 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; or online utilities like this site ; and there are many others.) Insert the graph into the supplied Word Student Answer Form. Be sure to label and number the axes appropriately so that the graph matches the chosen and calculated values from above. 4. Using correct function transformation terminology, describe the transformation of the graph of Asia if its parent function is North America. Page 2 of 3 5. 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. 6. At what size, x (in megabytes), will the consumer ratings be equal to 0 in Asia? Show all the work details. 7. From both the ISP's and customers' perspectives, why do you think it is important to study the consumer ratings of an Internet Service Provider (ISP)? Justify 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 3 of 3