5. Ellen, a civil engineer, is designing a suspension bridge. There will be a suspnsion cable on each side of the bridge, with support wire hanging down from the cable at different distances, as shown in the table. Distance from the Centre of Bridge (m) 10 20 30 40 50 60 Length of Support Wire (m) 5.56 7.12 9.68 13.24 17.80 23.36
a) Plot the given data into graphing technology. What does the domain represent and what does the range represent in this situation? (1).
Domain: Range:
b) What type of function do you think would best represent this data, and why? (1)
f) Regardless of your answer in part (b), determine a quadratic regression function to model this data. Write your function below and give a sketch in the space provided. (2)
c) Using your regression equation, determine the length of a supporting wire that is 48m away from the centre of the bridge. Is this interpolation or extrapolation? Explain. (3)
d) Using the graph of your model, determine how far away a support wire is from the centre of the bridge if its length is 15m. (1)