Final answer:
To determine the function that models the cost to ship a package weighing x pounds, we use the given information to calculate the cost per pound and the fixed fee. After setting up equations based on the costs for shipping packages weighing 50 and 70 pounds, we find that the cost function is c(x) = 4x + 8, which does not match any of the provided options, indicating a likely typo in the question.
Step-by-step explanation:
To find which function models the cost c(x) that the company charges to ship a package weighing x pounds, we need to determine the cost per pound and the fixed fee. We have two pieces of information: a 50-pound package costs $208 and a 70-pound package costs $288. Let's write two equations to represent these scenarios:
- For the 50-pound package: c(50) = 50p + f = 208
- For the 70-pound package: c(70) = 70p + f = 288
Where p is the cost per pound and f is the fixed fee. Solving these equations simultaneously, we subtract the first equation from the second to eliminate f, which gives us:
Substituting p = 4 into one of the original equations to find f, we get:
- c(50) = 50(4) + f = 208
- 200 + f = 208
- f = 8
Therefore, the function that models the cost is c(x) = 4x + 8, which is none of the options provided. It seems there may be a typo in the question since the correct answer is not listed among the options.