A mobile plan charges a base monthly fee of $19.00 for the first 450 minutes of air time plus a charge of $0.45 for each additional minute.
Write a piecewise-defined linear function that calculates the monthly cost (in dollars) for using m minutes of air time.
C(m) = 

    	if 
  ≤ m ≤ 
 
    	if m > 
 


Let's define the cost function $ C(m) $ for the monthly mobile plan based on the number of minutes $ m $ used.

Given:

1. A base monthly fee of $19.00 for the first 450 minutes.
2. An additional charge of $0.45 for each minute over 450.

The piecewise function $ C(m) $ is:

\[
C(m) = 
\begin{cases} 
19.00 & \text{if } 0 \leq m \leq 450 \\
19.00 + 0.45(m - 450) & \text{if } m > 450 
\end{cases}
\]

### Explanation:

- **For $ 0 \leq m \leq 450 $**: The cost is constant at $19.00.
- **For $ m > 450 $**: The cost is $19.00 plus $0.45 for each additional minute beyond 450.

Let me know if you need more details or have any questions!

### Related Questions:
1. What would be the monthly cost for exactly 500 minutes?
2. How would the function change if the base fee was $25.00?
3. What is the cost for using 600 minutes?
4. How could we graph this piecewise function?
5. How does this function compare to a flat-rate mobile plan with unlimited minutes?

#### Tip:
When working with piecewise functions, be careful to define each segment's conditions accurately to avoid overlap.

A mobile plan charges a base monthly fee of $19.00 for the first 450 minutes of air time plus a charge of $0.45 for each additional minute. Write a piecewise-defined linear function that calculates the monthly cost (in dollars) for using m minutes of air time. C(m) = if ≤ m ≤ if m > 

Calculate monthly mobile plan costs with a piecewise-defined function based on air time usage. This problem covers algebraic concepts, including linear and piecewise functions. Understand the base fee and additional charges, suitable for Grades 8-10 students.

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