Suppose the rate of change of the number of Social Security beneficiaries (in millions per year) can be modeled by

where t is the number of years past 1950.

(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 t0 represent 1950.
(c) How well does the model fit the data?

Transcribed Image Text:

dB 0.07149(0.1t + 1)² – 0.67114(0.1t + 1) + 2.2016 dt Number Number of Beneficiaries of Beneficiaries Year (millions) Year (millions) 2.9 2000 2010 1950 44.8 1960 14.3 53.3 1970 25.2 2020 68.8 1980 35.1 2030 82.7 1990 39.5