Answer: C. $y=11(x-1)+13$

Explanation:1. Analyze the cost structure: The cost for the first book is a flat $$13$. For any additional books beyond the first, the cost is $$11$ per book.

2. Consider the number of additional books: If $x$ is the total number of books purchased: If $x=1$, the cost is $$13$. There are $0$ additional books. If $x>1$, the number of books after the first is $(x-1)$.

3. Formulate the cost for the additional books: The cost for these $(x-1)$ additional books is $11 \times (x-1)$ dollars.

4. Formulate the total cost y: The total cost $y$ is the sum of the cost for the first book and the cost for the additional books. Total cost $y = (\text{cost of first book}) + (\text{cost of additional books})$ $y = 13 + 11(x-1)$ This can also be written as $y = 11(x-1) + 13$.

5. Check the equation for different values of x (and $x>0$): If $x=1$ (one book): $y = 11(1-1) + 13 = 11(0) + 13 = 0 + 13 = 13$. This is correct, as the first book costs $$13$. If $x=2$ (two books): The first book costs $$13$, the second (additional) book costs $$11$. Total = $$13 +$11 = $24$. Using the formula: $y = 11(2-1) + 13 = 11(1) + 13 = 11 + 13 = 24$. This is correct. If $x=3$ (three books): Cost = $$13 +$11 + 11 = \35$. Using the formula:$y = 11(3-1) + 13 = 11(2) + 13 = 22 + 13 = 35$. This is correct.

6. Compare with the given options: Our derived equation is $y = 11(x-1) + 13$. This matches option [C].

7. Conclusion: The equation that describes the situation is $y=11(x-1)+13$.