As the 76 million Americans born between 1946 and 1964 (the “baby boomers”) continue to age, the United States will see an increasing proportion of Americans who are within one year of a retirement age of 66. The model gives the projected rate of change in the number of people within one year of retirement, where t is the number of years since 1940, data from 1940 through 2050. See the figure.
(Source: Based on data from the U.S. Bureau of the Census)
a). Use a limit of sums to estimate to two decimal places the area of the region between the graph of r and the t-axis from t = 65 to t = 75. Show a numerical estimation tables starting with 5 subintervals and incrementing by × 2.
b). Write a sentence of interpretation for the result in part a.
