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 C(x)C(x) in terms of the number of movie channels xx.

  • 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:

C(x)=5x+23C(x) = 5x + 23

Where:

  • xx is the number of movie channels,
  • 5x5x 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:

  1. How would the cost function change if the base service fee was $30 instead of $23?
  2. What if the company introduced a discount for multiple movie channels? How would that affect the cost function?
  3. How can we interpret the slope of the cost function in real-life terms?
  4. How would you calculate the total cost if someone subscribes to 3 movie channels?
  5. 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

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Suitable Grade Level

Grades 7-9