Textbook Problem

Social Security beneficiaries The table gives the number of millions of Social Security beneficiaries (actual and projected) for selected years from 1950 through 2030.

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

Source: Social Security Trustees Report

With B(t) representing the number of beneficiaries (in millions) t years past 1950, these data can be modeled by the function

$B\left(t\right)=\left(0.01t+3\right)\left(0.0238t^2-9.79t+3100\right)-9290$

(a) Find the function that gives the instantaneous rate of change of the number of beneficiaries.

(b) Find and interpret the instantaneous rate of change in 2020.

(c) Use the data to determine which of the average rates of change (from 2010 to 2020, from 2020 to 2030, or from 2010 to 2030) best approximates the instantaneous rate from part (b).