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

To create the correct piecewise function for the cell phone plan charges, we need to define the cost based on the number of minutes used:

1. For 0 to 60 minutes (including 60), the charge is a flat rate of $15.00.
2. For any time greater than 60 minutes up to 63 minutes, the charge starts at $15.00 for the first 60 minutes, and then it adds $0.50 for every additional minute beyond 60.

Given the above conditions, the correct piecewise function can be expressed as:

\[ f(t) = \begin{cases} 15.00 & \text{if } 0 \leq t \leq 60 \ 15.00 + 0.50(t - 60) & \text{if } 60 < t \leq 63 \end{cases} \]

However, this can be simplified to:

\[ f(t) = \begin{cases} 15.00 & \text{if } 0 \leq t \leq 60 \ 0.50t - 15.00 & \text{if } 60 < t \leq 63 \end{cases} \]

This matches the description given, particularly focusing on adding $0.50 for each minute after the first 60.

From the options you've provided, the correct choice is:

f(t) = 15.00, 0 ≤ t ≤ 60; 0.50t - 15.00, 60 < t ≤ 63.