Part 1 of 3

A telephone company offers a monthly cellular phone plan for \[tex]$19.99. It includes 350 anytime minutes plus \$[/tex]0.20 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]\[
C(x)=\left\{\begin{array}{ll}
19.99 & \text{if } 0\ \textless \ x \leq 350 \\
0.20x - 50.01 & \text{if } x \ \textgreater \ 350
\end{array}\right.
\][/tex]

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

(a) 215 \\
(b) 410 \\
(c) 351

(a) [tex]\(C(215) = \$ \ \square\)[/tex] (Round to the nearest cent as needed.)



Answer :

To compute the monthly cost of the cellular phone for 215 anytime minutes used, we need to evaluate the function [tex]\( C(x) \)[/tex] at [tex]\( x = 215 \)[/tex].

Given the cost function:
[tex]\[ C(x) = \begin{cases} 19.99 & \text{if } 0 < x \leq 350 \\ 0.20 x - 50.01 & \text{if } x > 350 \end{cases} \][/tex]

For [tex]\( x = 215 \)[/tex], since [tex]\( 0 < 215 \leq 350 \)[/tex], the cost falls within the first condition of the piecewise function.

Thus,
[tex]\[ C(215) = 19.99 \][/tex]

Therefore, the monthly cost for using 215 anytime minutes is:
[tex]\[ C(215) = \$19.99 \][/tex]