The amounts f (t) (in billions of dollars) of child support collected in the United States from 2005 through 2014 can be approximated by the model
f (t) = −0.056t2 + 1.62t + 16.4, 5 ≤ t ≤ 14
Where t represents the year, with t = 5 corresponding to 2005.
(a) You want to adjust the model so that t = 5 corresponds to 2010 rather than 2005. To do this, you shift the graph of f five units to the left to obtain g(t) = f (t + 5). Use binomial coefficients to write g(t) in standard form.
(b) Use a graphing utility to graph f and g in the same viewing window.
(c) Use the graphs to estimate when the child support collections exceeded $27 billion.