Problem

A telephone company offers a monthly cellular phone plan for $\$ 34.99$. It includes 300 anytime minutes plus $\$ 0.25$ per minute for additional minutes. The following function is used to compute the monthly cost for a subscriber, where $\mathrm{x}$ is the number of anytime minutes used. \[ C(x)=\left\{\begin{array}{ll} 34.99 & \text { if } 0300 \end{array}\right. \] Compute the monthly cost of the cellular phone for use of the following anytime minutes. (a) 195 (b) 335 (c) 301

Solution

Step 1 :The problem provides a function to calculate the monthly cost of a cellular phone plan. The function is defined as follows: \[C(x)=\left\{\begin{array}{ll} 34.99 & \text { if } 0300 \end{array}\right.\] where \(x\) is the number of anytime minutes used.

Step 2 :We are asked to calculate the monthly cost for three different scenarios: (a) 195 minutes, (b) 335 minutes, and (c) 301 minutes.

Step 3 :For (a), since 195 is less than or equal to 300, we use the first part of the function. So, the cost is \$34.99.

Step 4 :For (b), since 335 is greater than 300, we use the second part of the function. So, the cost is \(0.25 \times 335 - 40.01 = \$43.74\).

Step 5 :For (c), since 301 is greater than 300, we use the second part of the function. So, the cost is \(0.25 \times 301 - 40.01 = \$35.24\).

Step 6 :Final Answer: The monthly cost of the cellular phone for use of 195 minutes is \(\boxed{34.99}\) dollars, for 335 minutes is \(\boxed{43.74}\) dollars, and for 301 minutes is \(\boxed{35.24}\) dollars.

From Solvely APP
Source: https://solvelyapp.com/problems/8166/

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