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A telephone company offers a monthly cellular phone plan for [tex]$\$[/tex]24.99[tex]$. It includes 350 anytime minutes plus $[/tex]\[tex]$0.25$[/tex] per minute for additional minutes. The following function is used to compute the monthly cost for a subscriber, where [tex]$x$[/tex] is the number of anytime minutes used.

[tex]\[
C(x) = \begin{cases}
24.99 & \text{if } 0 \ \textless \ x \leq 350 \\
0.25x - 62.51 & \text{if } x \ \textgreater \ 350
\end{cases}
\][/tex]

Compute the monthly cost of the cellular phone for the use of the following anytime minutes:

(a) 230

(b) 405

(c) 351

(a) [tex]$C(230) = \$[/tex] \square[tex]$ (Round to the nearest cent as needed.)

(b) $[/tex]C(405) = \[tex]$ \square$[/tex] (Round to the nearest cent as needed.)

(c) [tex]$C(351) = \$[/tex] \square$ (Round to the nearest cent as needed.)



Answer :

GinnyAnswer
Let's break down each part of the question to compute the monthly cost for different amounts of anytime minutes used.

### Part (a) [tex]\( C(230) \)[/tex]

Given:
- The subscriber uses 230 minutes.
- The first 350 minutes are included in the fixed monthly cost of [tex]$24.99. According to the provided function: - Since \( 230 \leq 350 \), the cost for 230 minutes is simply the fixed monthly cost: \[ C(230) = 24.99 \] Thus: \[ C(230) = \$[/tex] 24.99 \]

### Part (b) [tex]\( C(405) \)[/tex]

Given:
- The subscriber uses 405 minutes.
- The first 350 minutes are included in the fixed monthly cost of [tex]$24.99. - Additional minutes cost $[/tex]0.25 per minute.

According to the provided function:
- Since [tex]\( 405 > 350 \)[/tex], we use the second part of the function:
[tex]\[ C(405) = 0.25 \times 405 - 62.51 \][/tex]

Calculate the cost:
[tex]\[ C(405) = 0.25 \times 405 - 62.51 \][/tex]
[tex]\[ C(405) = 101.25 - 62.51 \][/tex]
[tex]\[ C(405) = 38.74 \][/tex]

Thus:
[tex]\[ C(405) = \$ 38.74 \][/tex]

### Part (c) [tex]\( C(351) \)[/tex]

Given:
- The subscriber uses 351 minutes.
- The first 350 minutes are included in the fixed monthly cost of [tex]$24.99. - Additional minutes cost $[/tex]0.25 per minute.

According to the provided function:
- Since [tex]\( 351 > 350 \)[/tex], we use the second part of the function:
[tex]\[ C(351) = 0.25 \times 351 - 62.51 \][/tex]

Calculate the cost:
[tex]\[ C(351) = 0.25 \times 351 - 62.51 \][/tex]
[tex]\[ C(351) = 87.75 - 62.51 \][/tex]
[tex]\[ C(351) = 25.24 \][/tex]

Thus:
[tex]\[ C(351) = \$ 25.24 \][/tex]

### Summary of the results:
(a) [tex]\( C(230) = \$ 24.99 \)[/tex] (rounded to the nearest cent)
(b) [tex]\( C(405) = \$ 38.74 \)[/tex] (rounded to the nearest cent)
(c) [tex]\( C(351) = \$ 25.24 \)[/tex] (rounded to the nearest cent)

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