Math Problem Statement
Solution
The problem in the image describes a telephone company charging a flat rate of $30 per month with 200 free call minutes, after which the company charges $0.03 per minute.
a) Write the function using function notation.
Let's define the function , where represents the total monthly cost, and is the total number of call minutes used in a month.
- For the first 200 minutes, the cost is fixed at $30.
- For any additional minutes beyond 200, there is an additional charge of $0.03 per minute.
Thus, the function can be written as:
\begin{cases} 30 & \text{if } x \leq 200, \\ 30 + 0.03(x - 200) & \text{if } x > 200. \end{cases}$$ This piecewise function represents the monthly charge based on the number of minutes used. Do you need further clarification or details? ### Related questions: 1. How would the function change if the charge per minute after 200 minutes was different? 2. What would the function look like if there was no fixed $30 monthly fee but only a per-minute charge? 3. How can this function be graphed, and what does the graph represent? 4. What happens to the total cost if a user makes exactly 200 minutes of calls? 5. How can we express this cost function using a single algebraic expression (without piecewise)? ### Tip: When working with piecewise functions, always remember to carefully consider the boundary conditions, such as the point where the pricing changes from a flat rate to per-minute charges.Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Algebra
Piecewise Functions
Formulas
C(x) = 30 for x ≤ 200, C(x) = 30 + 0.03(x - 200) for x > 200
Theorems
Piecewise function definitions
Suitable Grade Level
Grades 9-12
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