The numbers of millions of Social Security beneficiaries for selected years from 1950 and projected to 2030 are given in the following table.

(a) Find the cubic function that models these data, with x equal to the number of years past 1950. Report the model with 3 significant digits.

(b) Find the point of inflection of the graph of the reported model for x > 0.

(c) Graph this function and discuss what the point of inflection indicates.

Transcribed Image Text:

Number of Number of Beneficiaries Beneficiaries Year (millions) Year (millions) 1950 2.9 2000 45.2 1960 14.3 2010 53.4 1970 25.2 2020 69.1 1980 35.1 2030 84.7 1990 39.5