1. The problem is to simplify the expression for $f$ given by: $$f = 15 \times \frac{15}{10} b + 9.24$$ 2. The formula involves multiplication and addition. We will first simplify the multiplication part. 3. Simplify the fraction multiplication: $$15 \times \frac{15}{10} b = \frac{15 \times 15}{10} b = \frac{225}{10} b$$ 4. Simplify the fraction by canceling common factors: $$\frac{\cancel{225}^{\times 15}}{\cancel{10}^{\times 2}} b = \frac{45}{2} b$$ 5. Substitute back into the expression: $$f = \frac{45}{2} b + 9.24$$ 6. This is the simplified form of the function $f$ in terms of $b$. Final answer: $$f = \frac{45}{2} b + 9.24$$