Math Problem Statement
Write a cost function for the problem. Assume that the relationship is linear.
A cable TV company charges $23 for the basic service plus $5 for each movie channel. Let C(x) be the total cost in dollars of subscribing to cable TV, using x movie channels.
Question 5Select one:
A.
C(x) = 5x + 23
B.
C(x) = 23x + 5
C.
C(x) = 5x - 23
D.
C(x) = 23x - 5
Solution
The problem states that the cable TV company charges $23 for the basic service plus $5 for each movie channel. We are asked to express the total cost in terms of the number of movie channels .
- The base fee is $23 (which is constant).
- For each movie channel, the company charges an additional $5.
So, the cost function is given by the sum of the fixed base fee and the variable cost per movie channel, which is:
Where:
- is the number of movie channels,
- represents the cost of the movie channels, and
- 23 is the base fee.
Therefore, the correct answer is:
A. C(x) = 5x + 23
Would you like more details on how to derive such cost functions? Here are some related questions:
- How would the cost function change if the base service fee was $30 instead of $23?
- What if the company introduced a discount for multiple movie channels? How would that affect the cost function?
- How can we interpret the slope of the cost function in real-life terms?
- How would you calculate the total cost if someone subscribes to 3 movie channels?
- Can the relationship between cost and the number of channels be modeled by a non-linear function?
Tip: Always check the structure of a cost function. A linear relationship means the cost increases or decreases at a constant rate.
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Math Problem Analysis
Mathematical Concepts
Linear Functions
Algebra
Cost Functions
Formulas
C(x) = 5x + 23
Theorems
-
Suitable Grade Level
Grades 7-9