A phone company charges its customers $50 or the first 500 minutes used each month. For any additional minutes used over the 500, the customer is charged an additional $.10 per minute. Find the piecewise function that describes this situation.
Group of answer choices
yeah
Let x represent the number of minutes used.
For the first 500 minutes, the cost is $50.
For any additional minutes over 500, the cost is $0.10 per minute.
Therefore, the piecewise function can be written as:
f(x) = { $50 if x ≤ 500
{ $50 + ($0.10 * (x - 500)) if x > 500
To find the piecewise function that describes the situation, we need to consider two cases: when the number of minutes used is 500 or less, and when the number of minutes used is more than 500.
Case 1: Minutes used ≤ 500
In this case, the customer is charged a flat rate of $50. Therefore, the function for this case is:
f(x) = 50
Case 2: Minutes used > 500
In this case, the customer is charged $50 for the first 500 minutes and an additional $0.10 per minute for any minutes used over 500. Let's call the number of minutes used over 500 "x". Therefore, the function for this case is:
f(x) = 50 + 0.10x
Combining both cases, the piecewise function that describes the situation is:
f(x) = {
50 for x ≤ 500,
50 + 0.10x for x > 500
}
f(x) =
50 for x <= 500
50 + 0.10(x-500) for x > 500