Example 7 A certain consumer good is priced at 120 yuan per piece. Without the collection of additional taxes, approximately 800,000 pieces are sold annually. If the government levies an additional tax, collecting \( r \) yuan for every 100 yuan sold (called a tax rate of \( r \% \)), then the annual sales volume will decrease by \( \frac{20}{3} r \) ten thousand pieces. To ensure that the tax collected annually from this business is no less than 2.56 million yuan, what should \( r \) be?
Let the annual sales volume be $x$ million pieces, then the annual sales revenue is $120x$ million yuan, and the tax collected from it is $120x \cdot r\%$ million yuan. Therefore, $120x \cdot r\% \geqslant 256$.
From the given information, $x=80-\frac{20}{3} r$, so $120\left(80-\frac{20}{3} r\right) \cdot r\% \geqslant 256$, simplifying to $r^2 - 12r + 32 \leqslant 0$, solving this yields $4 \leqslant r \leqslant 8$.
Answer: The tax rate $r\%$ should satisfy $4\% \leqslant r\% \leqslant 8\%$, to ensure that the annual tax revenue is no less than 256 million yuan.