The total numbers n (in millions) of miles for all public roadways in the United States

Chapter 1, Problem 79

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Civil  Engineering The total numbers n (in millions) of miles for all public roadways in the United States from 2000 through 2011 can be approximated by the model

                    \(n(t)=\left\{\begin{array}{ll} 0.0050 t^{2}+0.005 t+3.95, & 0 \leq t \leq 2 \\ 0.013 t+3.95, & 2<t \leq 11 \end{array}\right.\)

where t represents the year, with t = 0 corresponding to 2000. The actual numbers are shown in the bar graph. (Source: U.S. Federal Highway Administration)

                   

(a) Identify the independent and dependent variables and explain what they represent in the context of the problem.

(b) Use the table feature of a graphing utility to approximate the total number of miles for all public roadways each year from 2000 through 2011.

(c) Compare the values in part (b) with the actual values shown in the bar graph. How well does the model fit the data?

(d) Do you think the piecewise-defined function could be used to predict the total number of miles for all public roadways for years outside the domain? Explain your reasoning.

Text Transcription:

n(t) = { _0.013t + 3.95,     2 < t leq 11 ^0.0050t^2 + 0.005t + 3.95,    0 leq t leq 2

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