54. Social Security beneficiaries Suppose the rate of change of the number of Social Security beneficiaries (in millions per year) can be modeled by dB 0.07149(0.1t + 1)? – 0.67114(0.1t + 1) + 2.2016 %3D dt where t is the number of years past 1950. Number Number of Beneficiaries of Beneficiaries Year (millions) Year (millions) 1950 2.9 2000 44.8 1960 14.3 2010 53.3 1970 25.2 2020 68.8 1980 35.1 2030 82.7 1990 39.5 Source: Social Security Administration

54. Social Security beneficiaries Suppose the rate of change of the number of Social Security beneficiaries (in millions per year) can be modeled by dB 0.07149(0.1t + 1)? – 0.67114(0.1t + 1) + 2.2016 %3D dt where t is the number of years past 1950. Number Number of Beneficiaries of Beneficiaries Year (millions) Year (millions) 1950 2.9 2000 44.8 1960 14.3 2010 53.3 1970 25.2 2020 68.8 1980 35.1 2030 82.7 1990 39.5 Source: Social Security Administration

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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Concept explainers

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

Question

54. Social Security beneficiaries Suppose the rate of
change of the number of Social Security beneficiaries
(in millions per year) can be modeled by
dB
0.07149(0.1t + 1)2 – 0.67114(0.lt + 1) + 2.2016
%3D
dt
where t is the number of years past 1950.
Number
Number
of Beneficiaries
of Beneficiaries
Year
(millions)
Year
(millions)
1950
2.9
2000
44.8
1960
14.3
2010
53.3
1970
25.2
2020
68.8
1980
35.1
2030
82.7
1990
39.5
Source: Social Security Administration
(a) Use integration and the data point for 2000 to find
the function B(t) that models the millions of Social
Security beneficiaries.
(b) The data in the table give the millions of Social
Security beneficiaries for selected years from 1950
and projected to 2030. Graph B(t) from part (a)
with the data in the table; let t = 0 represent 1950.
(c) How well does the model fit the data?
%3D

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