Question

a telephone company offers a monthly cellular phone plan for $39.99. it includes 350 anytime minutes plus $0.25 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.

c(x) = \begin{cases} 39.99 & \text{if } 0 < x leq 350 \\ 0.25x - 47.51 & \text{if } x > 350 end{cases}

compute the monthly cost of the cellular phone for use of the following anytime minutes.

(a) 250
(b) 415
(c) 351

(a) ( c(250) = $ ) (round to the nearest cent as needed.)
(b) ( c(415) = $ ) (round to the nearest cent as needed.)
(c) ( c(351) = $ ) (round to the nearest cent as needed.)

Explanation:

Step1: Analyze \( C(250) \)

Given the piecewise function \( C(x)=

$$\begin{cases}39.99, & \text{if } 0 < x \leq 350 \\ 0.25x - 47.51, & \text{if } x > 350\end{cases}$$

\). For \( x = 250 \), since \( 0 < 250 \leq 350 \), we use the first part of the piecewise function. So \( C(250)=39.99 \).

Step2: Analyze \( C(415) \)

For \( x = 415 \), since \( 415>350 \), we use the second part of the piecewise function \( C(x)=0.25x - 47.51 \). Substitute \( x = 415 \) into the formula: \( C(415)=0.25\times415 - 47.51 \). First, calculate \( 0.25\times415 = 103.75 \). Then, \( 103.75 - 47.51 = 56.24 \).

Step3: Analyze \( C(351) \)

For \( x = 351 \), since \( 351>350 \), we use the second part of the piecewise function \( C(x)=0.25x - 47.51 \). Substitute \( x = 351 \) into the formula: \( C(351)=0.25\times351 - 47.51 \). First, calculate \( 0.25\times351 = 87.75 \). Then, \( 87.75 - 47.51 = 40.24 \).

Answer:

(a) \( C(250)=\$39.99 \)
(b) \( C(415)=\$56.24 \)
(c) \( C(351)=\$40.24 \)