Chapter 2.1, Problem 25E

World Military Expenditure The following chart shows total military and arms trade expenditure from 1992–2010 ( $t=0$ represents 1990).²

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

a. If you want to model the expenditure 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. $f\left(t\right)=4t^2-56t-1,300$

B. $f\left(t\right)=-4t^2-56t+1,300$

C. $f\left(t\right)=4t^2-56t+1,300$

D. $f\left(t\right)=-4t^2-56t-1,300$

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?