The data table at the lower right shows a car’s speed in miles per hour and the car’s fuel efficiency in miles per gallon for each speed. A quadratic regression equation that models this data is given by [math]m(x) = –0.0146x^2 + 1.1802x + 9.1356[/math], where [math]x[/math] is speed in mph and [math]m(x)[/math] is fuel efficiency in mpg. A scatter plot of the data with the graph of this model is shown. Use the given regression model to find the car’s fuel efficiency in miles per gallon when this car is traveling [math]31.1[/math] mph. Compare your answer to the data in the table. Do these values match? Then use the graph to estimate the speed(s) that will result in fuel efficiencies of about [math]25[/math] mpg and [math]40[/math] mpg. Use the model to check your estimates.
[list=1] [*]Use the regression model to find the fuel efficiency in miles per gallon when this car is traveling [math]31.1[/math] mph. [*]Compare your answer to the data in the table. [*]Use the graph to estimate the speed(s) that will result in fuel efficiency of about [math]25[/math] mpg. Use the model to check your estimates. [*]Use the model equation to check your estimate. [*]Use the graph to estimate the speed(s) that will result in a fuel efficiency of about [math]40[/math] mpg. [*]Use the model equation to check your result. [/list]