56. Paved roads Suppose the rate of change of the percent P of U.S. public roads that are paved can be modeled by dP 938.9 dt (0.0852t + 35.5)² percentage points per year, where t is the number of years past 1960. (b) For selected years from 1960 to 2008, the data in the table show the percent of U.S. public roads that are paved. Witht = 0 representing 1960, graph these data and the model found in part (a). (c) Find the model's predicted percent for 2015. Year % Paved Year % Paved 1960 34.7 1995 60.8 1965 39.4 2000 63.4 1970 44.5 2002 64.8 1975 48.3 2004 64.5 1980 53.7 2006 65.2 1985 54.7 2008 67.4 1990 58.3 Source: U.S. Bureau of Transportation Statistics (a) Use integration and the data point for 2000 to find the function P(t) that models the percent of public roads that are paved.

56. Paved roads Suppose the rate of change of the percent P of U.S. public roads that are paved can be modeled by dP 938.9 dt (0.0852t + 35.5)² percentage points per year, where t is the number of years past 1960. (b) For selected years from 1960 to 2008, the data in the table show the percent of U.S. public roads that are paved. Witht = 0 representing 1960, graph these data and the model found in part (a). (c) Find the model's predicted percent for 2015. Year % Paved Year % Paved 1960 34.7 1995 60.8 1965 39.4 2000 63.4 1970 44.5 2002 64.8 1975 48.3 2004 64.5 1980 53.7 2006 65.2 1985 54.7 2008 67.4 1990 58.3 Source: U.S. Bureau of Transportation Statistics (a) Use integration and the data point for 2000 to find the function P(t) that models the percent of public roads that are paved.

Algebra and Trigonometry (MindTap Course List)

4th Edition

ISBN:9781305071742

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter1: Equations And Graphs

Section1.2: Graphs Of Equations In Two Variables; Circles

Problem 111E

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Question

56. Paved roads Suppose the rate of change of the percent
P of U.S. public roads that are paved can be modeled by
dP
938.9
dt
(0.0852t + 35.5)²
percentage points per year, where t is the number of
years past 1960.
(b) For selected years from 1960 to 2008, the data in
the table show the percent of U.S. public roads that
are paved. Witht = 0 representing 1960, graph
these data and the model found in part (a).
(c) Find the modelľ's predicted percent for 2015.
Year
% Paved
Year
% Paved
1960
34.7
1995
60.8
1965
39.4
2000
63.4
1970
44.5
2002
64.8
1975
48.3
2004
64.5
1980
53.7
2006
65.2
1985
54.7
2008
67.4
1990
58.3
Source: U.S. Bureau of Transportation Statistics
(a) Use integration and the data point for 2000 to find
the function P(t) that models the percent of public
roads that are paved.

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