The table shows the estimated average numbers of hours H that adults in the United

Chapter 3, Problem 20

(choose chapter or problem)

Modeling Data The table shows the estimated average numbers of hours H that adults in the United States spent reading newspapers each year from 2003 through 2012. (Source: Statista)

               

(a) Use a graphing utility to create a scatter plot of  the data. Let t represent  the year, with t = 3  corresponding to 2003.

(b) A cubic model for the data is

         \(H=0.131 t^{3}-2.81 t^{2}+12.1 t+183\)

which has an \(r^{2}\)-value of 0.9962. Use the graphing utility to graph the model with the scatter plot from part (a). Is the cubic model a good fit for the data? Explain.

(c) Use the regression feature of the graphing utility to find a quadratic model for the data and identify the coefficient of determination.

(d) Use the graphing utility to graph the quadratic model with the scatter plot from part (a). Is the quadratic model a good fit for the data? Explain.

(e) Which model is a better fit for the data? Explain.

(f) A consumer research company makes projections about the average numbers of hours H* that adults spent reading newspapers each year from 2013 through 2015. The company’s projections are shown in the table. Use the models from parts (b) and (c) to predict the average numbers of hours for 2013 through 2015. Explain why your values may differ from those in the table.

               

Text Transcription:

H = 0.131t^3 - 2.81t^2 + 12.1t + 183

r^2