The table gives the thousands of U.

The table gives the thousands of U.S. workers who were union members for selected years from 1930 to 2009.

Year

Members

Year

Members

1930

3401

1975

19,611

1935

3584

1980

19,843

1940

8717

1985

16,996

1945

14,322

1990

16,740

1950

14,267

1995

16,360

1955

16,802

2000

16,258

1960

17,049

2005

15,685

1965

17,299

2009

16,904

1970

19,381

(a) With t 5 0 representing 1900, find a cubic function that models these data.

(b) Find the critical values for the model and classify them.

(c) How well does the relative maximum from the model agree with the data?

(d) Do you think that union membership will reach a minimum and then increase as the model predicts? Explain.