55. Females in the work force Suppose the rate of change of the percent p of total U.S. workers who are female can be modeled by dp (1.38t + 64.1)2 2154.18 %3D dt percentage points per year, where t is the number of years past 1950. Year % Female Year % Female 950 29.6 2010 47.9 960 33.4 2015 48.3 970 38.1 2020 48.1 980 42.5 2030 48.0 45.2 2040 47.9 066 000 46.6 2050 47.9 ource: U.S. Census Bureau (a) Use integration and the data point for 2040 to find the function p(t) that models the percent of the work force that is female. (b) For selected years from 1950 and projected to 2050, the data in the table show the percent of total U.S. workers who are female. With t as the number of years past 1950, graph these data with the model found in part (a). (c) Comment on the model's fit to the data

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Chapter2: Second-order Linear Odes
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55. Females in the work force Suppose the rate of change
of the percent p of total U.S. workers who are female
can be modeled by
dp
(1.38t + 64.1)?
2154.18
dt
percentage points per year, where t is the number of
years past 1950.
Year
% Female
Year
% Female
1950
29.6
2010
47.9
1960
33.4
2015
48.3
1970
38.1
2020
48.1
1980
42.5
2030
48.0
1990
45.2
2040
47.9
2000
46.6
2050
47.9
Source: U.S. Census Bureau
(a) Use integration and the data point for 2040 to find
the function p(t) that models the percent of the
work force that is female.
(b) For selected years from 1950 and projected to
2050, the data in the table show the percent of total
U.S. workers who are female. With t as the number
of years past 1950, graph these data with the model
found in part (a).
(c) Comment on the modeľ's fit to the data.
Transcribed Image Text:55. Females in the work force Suppose the rate of change of the percent p of total U.S. workers who are female can be modeled by dp (1.38t + 64.1)? 2154.18 dt percentage points per year, where t is the number of years past 1950. Year % Female Year % Female 1950 29.6 2010 47.9 1960 33.4 2015 48.3 1970 38.1 2020 48.1 1980 42.5 2030 48.0 1990 45.2 2040 47.9 2000 46.6 2050 47.9 Source: U.S. Census Bureau (a) Use integration and the data point for 2040 to find the function p(t) that models the percent of the work force that is female. (b) For selected years from 1950 and projected to 2050, the data in the table show the percent of total U.S. workers who are female. With t as the number of years past 1950, graph these data with the model found in part (a). (c) Comment on the modeľ's fit to the data.
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