Chapter 2.2, Problem 45E

Pension resources The Pension Benefit Guaranty Corporation is the agency that insures pension. The figure shows one study’s projection for the agency’s total resources, initially rising (from taking over the assets of failing plans) but then falling (as more workers retire and payouts increase).

What kind of function might be used to model the agency’s total resources ?

If a function of the form $f(x)=a{x}^2+bx+c$ were used to model these total resources. would $f(x)$ have $a>0$ or $a<0$? Explain.

If the model from part (b) used $x$ as the number of years past $2004$, explain way the model would have $b>0$ and $c>0$.

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