Question

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).

Type your answer in the form with NO SPACES.

�(�)={��1 ; ������1��2 ; ������2C\left(t\right)=\left\{\begin{array}{l}Eq_1\ ;\ domain_1\\Eq_2\ ;\ domain_2\end{array}\right.C(t)={
Eq
1
​
; domain
1
​

Eq
2
​
; domain
2
​

​

Answer 1

The cost function C(t) for the cell phone plan is piecewise-defined by C(t) = 40 for 0 ≤ t ≤ 400 and C(t) = 40 + 0.50(t - 400) for t > 400, representing a flat rate for the first 400 minutes and an additional charge per minute thereafter.

Step-by-step explanation:

The cost C(t) for a phone plan that charges $40 for the first 400 minutes and an additional $0.50 for every minute over 400 can be represented by a piecewise-defined function. The variable t represents the total talk time in minutes. This function has two parts, which correlate to the two different rates that are being charged depending on whether the talk time is within the first 400 minutes or beyond that.

For the first 400 minutes, there is a flat rate, so the cost remains constant at $40. However, once the talk time exceeds 400 minutes, each additional minute adds $0.50 to the total cost.

The piecewise-defined function for the cost C(t) is as follows:

C(t) = {

40 ; if 0 ≤ t ≤ 400

40 + 0.50(t - 400) ; if t > 400

}