Answer: C. $y=14(x-1)+16$

Explanation:1. Analyze the cost structure: - Cost for the first book: $$16$ (this applies if $x \ge 1$). - Cost for each additional book (any book after the first): $$14$.

2. Determine the number of additional books: If $x$ is the total number of books purchased: - If $x=1$, there are $0$ additional books. - If $x>1$, the number of additional books is $(x-1)$.

3. Formulate the cost of the additional books: The cost for $(x-1)$ additional books, each costing $$14$, is $14 \times (x-1)$ dollars. This term is only applicable if $x>1$. If $x=1$, this term is $14(1-1)=0$.

4. Formulate the total cost y: The total cost $y$ is the sum of the cost for the first book and the cost for any additional books. Total cost $y = (\text{cost of first book}) + (\text{cost of additional books})$ $y = 16 + 14(x-1)$ This can also be written as $y = 14(x-1) + 16$.

5. Verify the equation for some values of x (given $x>0$): - If $x=1$ (one book): $y = 14(1-1) + 16 = 14(0) + 16 = 0 + 16 = 16$. This is correct. - If $x=2$ (two books): Cost should be $$16$ (for first) + $$14$ (for second) = $$30$. Using the formula: $y = 14(2-1) + 16 = 14(1) + 16 = 14 + 16 = 30$. This is correct. - If $x=3$ (three books): Cost should be $$16 +$14 + 14 = \44$. Using the formula:$y = 14(3-1) + 16 = 14(2) + 16 = 28 + 16 = 44$. This is correct.

6. Check the solution with the options: Our derived equation is $y = 14(x-1) + 16$. This matches option [C].

7. Conclusion: The equation that describes this situation is $y=14(x-1)+16$.