Speed cell wireless offers a plan of $40 for the first 400 minutes and an additional 0.50 for every minute over 400. Let t represent the total talk time in minutes. Write a piecewise -defined function to represent the cost C(T)
To write a piecewise-defined function for the cost C(t) based on the given information, we need to define different cases.
Case 1: When the total talk time, t, is less than or equal to 400 minutes, the cost is $40. This is because within the first 400 minutes, the cost remains constant.
Case 2: When the total talk time, t, exceeds 400 minutes, the cost is calculated by adding an additional $0.50 for every minute over 400. So, we can use the formula C(t) = $40 + ($0.50 * (t - 400)).
By combining these two cases, we can form a piecewise-defined function to represent the cost C(t):
C(t) = {
$40 if t ≤ 400,
$40 + ($0.50 * (t - 400)) if t > 400
}
This function represents the cost, C(t), in terms of the total talk time, t, based on the provided pricing structure.