Modeling Economic Dependency Ratio

The economic dependency ratio is defined as the number of persons in the total population who are not in the work force per 100 in the work force. Since 1960, Baby Boomers in the work force 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.

(b) Use the result 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).