53. Poverty line Suppose the rate of change of the number of people (in millions) in the United States who lived below the poverty level can be modeled by dp = -0.0005728(2t + 3)³ + 0.04452(2t + 3)² dt - 0.9744(2t + 3) + 5.572 where t is the number of years past 1990. Persons below Persons below the Poverty Level (millions) the Poverty Level (millions) Year Year 1991 35.7 2000 31.1 1992 38.0 2002 34.6 1993 39.3 2003 35.9 1994 38.1 2004 37.0 1995 36.4 2005 37.0 1996 36.5 2006 36.5 1997 35.6 2007 37.2 1998 34.5 2008 39.8 1999 32.3 2009 43.6 Source: U.S. Bureau of the Census (a) Use integration and the data point for 2008 to find the function that models the number of people, in millions, in the United States who lived below the poverty level. (b) The data in the table show the numbers of people, in millions, in the United States who lived below the poverty level for selected years. Graph the function from part (a) with the data in the table with t = 0 representing 1990. (c) How well does the model fit the data?

53. Poverty line Suppose the rate of change of the number of people (in millions) in the United States who lived below the poverty level can be modeled by dp = -0.0005728(2t + 3)³ + 0.04452(2t + 3)² dt - 0.9744(2t + 3) + 5.572 where t is the number of years past 1990. Persons below Persons below the Poverty Level (millions) the Poverty Level (millions) Year Year 1991 35.7 2000 31.1 1992 38.0 2002 34.6 1993 39.3 2003 35.9 1994 38.1 2004 37.0 1995 36.4 2005 37.0 1996 36.5 2006 36.5 1997 35.6 2007 37.2 1998 34.5 2008 39.8 1999 32.3 2009 43.6 Source: U.S. Bureau of the Census (a) Use integration and the data point for 2008 to find the function that models the number of people, in millions, in the United States who lived below the poverty level. (b) The data in the table show the numbers of people, in millions, in the United States who lived below the poverty level for selected years. Graph the function from part (a) with the data in the table with t = 0 representing 1990. (c) How well does the model fit the data?

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

53. Poverty line Suppose the rate of change of the number
of people (in millions) in the United States who lived
below the poverty level can be modeled by
dp
= -0.0005728(2t + 3)³ + 0.04452(2t + 3)²
dt
- 0.9744(2t + 3) + 5.572
where t is the number of years past 1990.
Persons below
Persons below
the Poverty Level
(millions)
the Poverty Level
(millions)
Year
Year
1991
35.7
2000
31.1
1992
38.0
2002
34.6
1993
39.3
2003
35.9
1994
38.1
2004
37.0
1995
36.4
2005
37.0
1996
36.5
2006
36.5
1997
35.6
2007
37.2
1998
34.5
2008
39.8
1999
32.3
2009
43.6
Source: U.S. Bureau of the Census
(a) Use integration and the data point for 2008 to find
the function that models the number of people, in
millions, in the United States who lived below the
poverty level.
(b) The data in the table show the numbers of people,
in millions, in the United States who lived below
the poverty level for selected years. Graph the
function from part (a) with the data in the table
with t = 0 representing 1990.
(c) How well does the model fit the data?

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