A telephone company offers a monthly cellular phone plan for $ 24.99. It includes 350 anytime minutes plus $ 0.20 per minute for additional minutes. The following function is used to compute the monthly cost for a​ subscriber, where x is the number of anytime minutes used.
Upper C left parenthesis x right parenthesis equalsleft brace Start 2 By 2 Matrix 1st Row 1st Column 24.99 2nd Column if 0 less than x less than or equals 350 2nd Row 1st Column 0.20 x minus 45.01 2nd Column if x greater than 350 EndMatrix

Compute the monthly cost of the cellular phone for use of the following anytime minutes.
​(a) 205                    ​(b) 420                    ​(c) 351

The given function defines the monthly cost $ C(x) $ for a subscriber, based on the number of anytime minutes $ x $ used.

The function is as follows:

\[
C(x) = 
\begin{cases} 
24.99 & \text{if } 0 \leq x \leq 350 \\
0.20(x) - 45.01 & \text{if } x > 350 
\end{cases}
\]

### Let's compute the monthly cost for each scenario:

**(a) For $ x = 205 $:**

Since 205 is less than 350, we use the first part of the function:

\[
C(205) = 24.99
\]

**(b) For $ x = 420 $:**

Since 420 is greater than 350, we use the second part of the function:

\[
C(420) = 0.20(420) - 45.01
\]

Let's calculate that:

\[
C(420) = 0.20 \times 420 - 45.01 = 84 - 45.01 = 38.99
\]

**(c) For $ x = 351 $:**

Since 351 is greater than 350, we again use the second part of the function:

\[
C(351) = 0.20(351) - 45.01
\]

Let's calculate that:

\[
C(351) = 0.20 \times 351 - 45.01 = 70.20 - 45.01 = 25.19
\]

### Summary of costs:

- (a) $ x = 205 $: Cost = **$24.99**
- (b) $ x = 420 $: Cost = **$38.99**
- (c) $ x = 351 $: Cost = **$25.19**

Would you like more details, or do you have any questions?

### 5 Related Questions:
1. How is the slope of the cost function determined for additional minutes beyond 350?
2. What is the total cost if 400 minutes are used?
3. How would the function change if the rate for extra minutes was $0.25 instead of $0.20?
4. Can you represent the monthly cost function graphically?
5. What happens to the monthly cost if the anytime minutes are increased to 500?

### Tip:
When solving piecewise functions, always ensure you're using the correct part of the function for each input interval.

A telephone company offers a monthly cellular phone plan for $24.99. It includes 350 anytime minutes plus $0.20 per minute for additional minutes. The following function is used to compute the monthly cost for a subscriber, where x is the number of anytime minutes used. Compute the monthly cost of the cellular phone for use of the following anytime minutes: (a) 205, (b) 420, (c) 351.

Learn how to compute the monthly cost for a cellular phone plan using a piecewise function. This problem explores the calculation of costs for 205, 351, and 420 anytime minutes. Ideal for high school students studying linear equations and piecewise functions.

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