
(a)
To calculate: The function for the instantaneous rate of change of the number of beneficiaries, if the function for the number of beneficiaries (in millions) t years past 1950 model as
Year | Number of Beneficiaries (millions) | Year | Number of Beneficiaries (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 |
(b)
To calculate: The instantaneous rate of change of the number of beneficiaries in 2020 and its interpretation, if the function for the number of beneficiaries (in millions) t years past 1950 model as
The data that gives the number of Social Security beneficiaries (actual and projected) for selected years from 1950 through 2030 for which the function is modeled is tabulated below
Year | Number of Beneficiaries (millions) | Year | Number of Beneficiaries (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 |
(c)
The time range among (from 2010 to 2020, from 2020 to 2030 orfrom 2010 to 2030) for which the average rate of change is the best approximates of the instantaneous rate of change in 2020, if the function for the number of beneficiaries (in millions) t years past 1950 model as
The data that gives the number of Social Security beneficiaries (actual and projected) for selected years from 1950 through 2030 for which the function is modeled is tabulated below
Year | Number of Beneficiaries (millions) | Year | Number of Beneficiaries (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 |

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