The table shows the numbers of commercial FM radio stations S in the United States from

Chapter 3, Problem 123

(choose chapter or problem)

Modeling Data The table shows the numbers of commercial FM radio stations S in the United States from 2004 through 2013. (Source: Federal Communications Commission)

                           

(a) Use a graphing utility to create a scatter plot of the data. Let t represent the year, with t = 4 corresponding to 2004.

(b) A cubic model for the data is

     \(S=-1.088 t^{3}+26.61 t^{2}-150.9 t+6459\)

     Use the graphing utility to graph this model with the scatter plot from part (a)

(c) Use the regression feature of the graphing utility to find a quadratic model for the data. Then graph the model with the scatter plot from part (a).

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

(e) Use the model you chose in part (d) to predict the number of commercial FM radio stations in 2015.

Text Transcription:

S = -1.088t^3 + 26.61t^2 - 150.9t + 6459