The data in the accompanying table show the speed n (in increments of 5 mph) of an autom...

The data in the accompanying table show the speed n (in increments of 5 mph) of an automobile and the associated distance a_n in feet required to stop it once the brakes are applied. For instance, n = 6 (representing 6 × 5 = 30 mph) requires a stopping distance of a₆ = 47 ft.

a. Calculate and plot the change Δa_nversus n. Does the graph reasonably approximate a linear relationship?

b. Based on your conclusions in part (a), find a difference equation model for the stopping distance data. Test your model by plotting the errors in the predicted values against n. Discuss the appropriateness of the model.