Question

A cell phone plan charges $15.00 for the first 60 minutes or less used in a month and $0.50 for each additional minute or portion of a minute. Select the piecewise function that shows the charges for time t where t ranges from 0 to 63 minutes. (1 point)
Responses

f(t)={15.00,0.50t−15.00,0≤t≤6060<t≤63)

f ( t ) = 15 . 00 , 0 ≤ t ≤ 60 0 . 50 t - 15 . 00 , 60 < t ≤ 63

f(t)={15.00,15.00+0.50t,0≤t≤6060<t≤63)
f ( t ) = 15 . 00 , 0 ≤ t ≤ 60 15 . 00 + 0 . 50 t , 60 < t ≤ 63

f⎛⎝⎜⎜⎜t⎞⎠⎟⎟⎟=⎧⎩⎨⎪⎪⎪⎪⎪⎪⎪⎪15.00,15.50,16.00,16.50,0≤t≤6060<t≤6161<t≤6262<t≤63⎞⎠⎟⎟⎟

f ( t ) = 15 . 00 , 0 ≤ t ≤ 60 15 . 50 , 60 < t ≤ 61 16 . 00 , 61 < t ≤ 62 16 . 50 , 62 < t ≤ 63

f⎛⎝⎜⎜⎜t⎞⎠⎟⎟⎟=⎧⎩⎨⎪⎪⎪⎪⎪⎪⎪⎪15.00,15.50−0.50t,16.00−0.50t,16.50−0.50t,0≤t≤6060<t≤6161<t≤6262<t≤63⎞⎠⎟⎟⎟

Answer 1

The cell phone plan can be defined as a piecewise function based on the usage of minutes. Here's how the charges work:

1. For the first 60 minutes (0 ≤ t ≤ 60), the charge is a flat fee of $15.00.
2. 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.