The economic dependency ratio is defined as the number of persons in the total population who are not in the workforce per 100 in the workforce. Since 1960, Baby Boomers in the workforce coupled with a decrease in the birth rate have caused a significant decrease in the economic dependency ratio.
The table shows the economic dependency ratio for selected years from 1960 and projected to 2050.

(a) Model these data with a cubic function, R(x), where R(x) is the economic dependency ratio and x is the number of years past 1950. Report the model with three significant digit coefficients.
(b) Use the reported model from part (a) to find the function that models the rate of change of R(x).
(c) Find the function that gives the rate of change of R'(x).
(d) Find and interpret R'(90) and R"(90).

Transcribed Image Text:

Ratio Year Year Ratio 1960 150.4 2015 91.9 140.4 97.4 1970 2020 2030 1980 108.9 106.4 1990 98.3 2040 109.0 2000 2050 93.9 111.4 2010 90.3