Chapter 2.1, Problem 26E

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.)

Source: www.globalissues.org/Geopolitics/ArmsTrade/Spending.asp

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

$f\left(t\right)=a{t}^2+bt+c$, would you expect the coefficient a to be positive or negative? Why? [HINT: See “Features of a Parabola” in this section.]

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

A. $f\left(t\right)=0.04t^2+0.3t-6$

B. $f\left(t\right)=-0.04t^2+0.3t+6$

C. $f\left(t\right)=0.04t^2+0.3t+6$

D. $f\left(t\right)=-0.04t^2+0.3t-6$

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?