Final answer:
The cost function C(x) for the phone plan is a piecewise function where C(x) is $25 for 0 ≤ x ≤ 250 and $25 + $0.20(x - 250) for x > 250.
Step-by-step explanation:
The piecewise-defined function that represents the cost for using x minutes in a month for the given phone plan is:
C(x) = {
$25 & & if 0 ≤ x ≤ 250
$25 + $0.20(x - 250) & & if x > 250
}
Here, for the first 250 minutes, the cost is fixed at $25. For any usage above 250 minutes, an additional charge of $0.20 per minute is applied. This additional cost is only applied to the minutes used in excess of the included 250 minutes.
25: This is the fixed monthly fee for the plan. It applies when the user uses 250 minutes or less.
0.20: This is the additional charge per minute for exceeding the 250-minute limit.
x - 250: This is the number of minutes exceeding the 250-minute limit.
0.20(x - 250) + 25: This combines the fixed fee and the additional charges for exceeding the limit.