The table shows the numbers (in millions) of single women (never married) and married women m in the civilian work force in the United States for the years 2003 through 2010.

(a) Use the regression capabilities of a graphing utility to find a model of the form m(s) = as³ + bs² + cs + d for the data, where t is the time in years, with t = 3 corresponding to 2003.

(b) Find dm/dt. Then use the model to estimate dm/dt for
t = 7 when it is predicted that the number of single
women in the work force will increase at the rate of 0.75
million per year.

Transcribed Image Text:

Year S m Year S m 2003 18.4 36.0 2004 2005 2006 18.6 19.2 36.9 35.8 35.9 2007 19.7 20.2 2008 2009 37.2 20.2 37.3 19.5 36.3 2010 20.6 36.7