1. **Problem:** Given the function $c(x) = \frac{120 + 4x}{x}$ representing the average cost per book when printing $x$ copies, answer the following: 2. **Step 1: Calculate cost per book for 50 and 100 books.** - For $x=50$: $$c(50) = \frac{120 + 4(50)}{50} = \frac{120 + 200}{50} = \frac{320}{50} = 6.4$$ - For $x=100$: $$c(100) = \frac{120 + 4(100)}{100} = \frac{120 + 400}{100} = \frac{520}{100} = 5.2$$ 3. **Step 2: Write the equation for the horizontal asymptote.** - The horizontal asymptote is found by considering the behavior as $x \to \infty$: $$\lim_{x \to \infty} \frac{120 + 4x}{x} = \lim_{x \to \infty} \left( \frac{120}{x} + 4 \right) = 0 + 4 = 4$$ - So, the horizontal asymptote is: $$y = 4$$ 4. **Step 3: Interpret the end behavior in context.** - As the number of books printed increases, the average cost per book approaches 4 dollars. - This means the fixed cost of 120 dollars becomes negligible, and the cost per book is dominated by the variable cost of 4 dollars per book. **Final answers:** - Cost per book at 50 books: $6.4$ - Cost per book at 100 books: $5.2$ - Horizontal asymptote: $y = 4$ - End behavior interpretation: The average cost per book approaches 4 dollars as more books are printed, reflecting the variable cost per book.