(Answered) Social security beneficiariesthe table gives the number of

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Social Security beneficiaries

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

1314_Social Security beneficiaries.png

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

B(t) = (0.01t + 3)(0.02383t² - 9.79t + 3097.19) - 9289.371

(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 2010.

(c) Use the data to determine which of the average rates of change (from 2000 to 2010, from 2010 to 2020, or from 2000 to 2020) best approximates the instantaneous rate from part (b).

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