Education Expenditure The following table shows the percentage of the U.S....

Education Expenditure The following table shows the percentage of the U.S. Discretionary Budget allocated to education in 2003, 2005, and 2009. (See Exercise 20; t = 3 represents the start of 2003.)

Find a quadratic model for these data, and use your model to estimate the percentage of the U.S. Discretionary Budget allocated to education in 2008. Compare your answer with the actual figure shown in Exercise 20

Exercise 20:

Education Expenditure The following chart shows the percentage of the U.S. Discretionary Budget allocated to education from 2003 to 2009 (t = 3 represents the start of 2003).

a. If you want to model the percentage figures with a function of the form

would you expect the coefficient a to be positive or negative? Why? HINT [See “Features of a Parabola,” page 125.]

b. Which of the following models best approximates the data given? (Try to answer this without actually computing values)

c. What is the nearest year that would correspond to the vertex of the graph of the correct model from part (b)? What is the danger of extrapolating the data in either direction?