Data Analysis: Temperature The table shows the temperatures y (in degrees Fahrenheit) in a...

Data Analysis: Temperature The table shows the temperatures y (in degrees Fahrenheit) in a city over a 24-hour period. Let x represent the time of day, where x = 0 corresponds to 6 A.M.

A model that represents these data is given by

y = 0.026x3 − 1.03x2 + 10.2x +34, 0<x<24.

(a) Use a graphing utility to create a scatter plot of the data. Then graph the model in the same viewing window.

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(b) How well does the model fit the data?

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(c) Use the graph to approximate the times when the temperature was increasing and decreasing.

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(d) Use the graph to approximate the maximum and minimum temperatures during this 24-hour period.

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(e) Could this model predict the temperatures in the city during the next 24-hour period? Why or why not?