The table shows the average prices f (t) (in cents per kilowatt-hour) of residential electricity in the United States from 2007 through 2014.

(a) Use the regression feature of a graphing utility to find a cubic model for the data. Let t represent the year, with t = 7 corresponding to 2007.
(b) Use the graphing utility to plot the data and the model in the same viewing window.
(c) You want to adjust the model so that t = 7 corresponds to 2012 rather than 2007. To do this, you shift the graph of f five units to the left to obtain g(t) = f (t + 5). Use binomial coefficients to write g(t) in standard form.
(d) Use the graphing utility to graph g in the same viewing window as f.
(e) Use both models to predict the average price in 2015. Do you obtain the same answer?
(f) Do your answers to part (e) seem reasonable? Explain.
(g) What factors do you think contributed to the change in the average price?

Year Average Price, f() 2007 10.65 2008 11.26 2009 11.51 11.54 2010 2011 11.72 2012 11.88 2013 12.13 2014 12.52 Spreadsheet at Lars onPrecalculus com