The cell phone plan can be defined as a piecewise function based on the usage of minutes. Here's how the charges work:
- For the first 60 minutes (0 ≤ t ≤ 60), the charge is a flat fee of $15.00.
- For every minute over 60 (60 < t ≤ 63), the charge increases by $0.50 for each additional minute.
To define this as a piecewise function:
\[ f(t) = \begin{cases} 15.00 & \text{if } 0 \leq t \leq 60 \ 15.00 + 0.50(t - 60) & \text{if } 60 < t \leq 63 \end{cases} \]
This function states that for up to 60 minutes, the charge is $15.00. If the time exceeds 60 minutes, the charge is calculated as $15.00 plus $0.50 for each additional minute used over 60.
Thus, the correct piecewise function from the provided options is:
\[ f(t) = 15.00, , 0 \leq t \leq 60 \ 15.00 + 0.50(t - 60), , 60 < t \leq 63 \]
Comparing with the options, the most appropriate one is:
f(t) = 15.00, 0 ≤ t ≤ 60 \ 15.00 + 0.50t - 30, 60 < t ≤ 63
Which simplifies to:
f(t) = 15.00, 0 ≤ t ≤ 60 \ 0.50t - 15.00, 60 < t ≤ 63
This matches your question by representing the additional charges accurately for the required range of minutes.