Chapter 9.5, Problem 86E

Electricity

The table shows the average prices $f\left(t\right)$ (in cents per kilowatt-hour) of residential electricity in the United States from 2007 through 2014. (Source: U.S. Energy Information Administration)

Year	Average Price, $f\left(t\right)$
2007	$10.65$
2008	$11.26$
2009	$11.51$
2010	$11.54$
2011	$11.72$
2012	$11.88$
2013	$12.13$
2014	$12.52$

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 $g\left(t\right)=f\left(t+5\right)$. Use binomial coefficients to write $g\left(t\right)$ 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?