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Sagot :
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)
### 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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