Final answer:
The correct statement about the shipping rate is that shipping at the second rate will always cost $1.60 more than shipping at the first rate.
Step-by-step explanation:
The Quick Ship company uses the function C(w) = 0.45w + 0.35w + 1.6 if 0 < w ≤ 16, to calculate the cost in dollars, C, for shipping an item weighing w ounces. Let's analyze the given options to find the correct statement:
- A. It is possible that an item weighing less than 16 ounces could cost the same as an item weighing more than 16 ounces: This statement is false because the cost function is based on weight, and if the weight is higher, the cost will also be higher. Therefore, the cost of an item weighing more than 16 ounces will always be more than an item weighing less than 16 ounces.
- B. To find the charge for shipping a package weighing more than 16 ounces, multiply the weight by $0.035: This statement is false because the cost function does not have a constant rate for weights higher than 16 ounces. It includes a rate of $0.35 per ounce, plus an additional $1.60.
- C. Shipping at the second rate will always cost $1.60 more than shipping at the first rate: This statement is true. The cost function includes a constant term of $1.60, which means that regardless of the weight, shipping at the second rate will always cost $1.60 more than shipping at the first rate.
- D. If the weight is greater than 16 ounces, the shipping rate is $0.35 per ounce, plus $1.60: This statement is true. As mentioned earlier, the cost function includes a rate of $0.35 per ounce for weights greater than 16 ounces, plus an additional $1.60.
Based on the analysis, the correct statement is C. Shipping at the second rate will always cost $1.60 more than shipping at the first rate.