Textbook Problem

Modeling Data Outlays for national defense D (in billions of dollars) for 2006 through 2014 are shown in the table, where t is the time in years, with $t=6$ corresponding to2006. (Source: U.S. Office of Management and Budget)

T	6	7	8	9	10
D	521.8	551.3	616.1	661.0	693.5
t	11	12	13	14
D	705.6	677.9	633.4	603.5

(a) Use the regression capabilities of a graphing utility to find a model of the form

$D=a{t}^4+b{t}^3+c{t}^2+dt+e$

for the data.

(b) Use a graphing utility to plot the data and graph the model.

(c) For the years shown in the table, when does the model indicate that the outlay for national defense was at a

(d) For the years shown in the table, when does the model indicate that the outlay for national defense was increasing at the greatest rate?