Answer
$\text{(a)}$ Refer to the graph below. The highest interest rate was $8.67\%$ in $1997$.
$\text{(b)}$ $-10.343\%$, unreasonable since it is negative.
Work Step by Step
$\text{(a)}$ Use a graphing utility and input the function $r(x)=-0.115x^2+1.183x+5.623$ and set $0\le x\le 15$. Refer to the graph below..
From the graph, we can find the maximum at $r(5)\approx8.67$ which means the interest rate is $8.67\%$ in $1997$.
$\text{(b)}$ For year $2010$, $x=2010-1992=18$, thus $r(18)=-0.115(18)^2+1.183(18)+5.623\approx -10.343\%$.
This value is unreasonable because it is negative.
