The table shows the numbers (in millions) of participants in the free lunch program f and the reduced price lunch program r in the United States for the years 2007 through 2014. 

(a) Use the regression capabilities of a graphing utility to find a model of the form r(f) = af³ + bf² + cf + d for the data, where t is the time in years, with t = 7 corresponding to 2007.

(b) Find dr/dt. Then use the model to estimate dr/dt for t = 9 when it is predicted that the number of participants in the free lunch program will increase at the rate of 1.25 million participants per year.

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Year 2007 f r Year f r 15.0 3.1 2011 18.4 2008 15.4 16.3 3.1 2009 3.2 2012 2013 2.7 2.7 18.7 18.9 2.6 2010 17.6 3.0 2014 19.2 2.5