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).

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Answer 1

The cost C(t) of the wireless plan is a piecewise-defined function with two parts: $40 for t ≤ 400, and $40 + $0.50(t - 400) for t > 400.

Step-by-step explanation:

The cost C(t) of the Speed Cell Wireless plan can be represented by a piecewise-defined function, which changes based on the total talk time t in minutes.

The function has two parts: the flat rate cost when the talk time is equal to or less than 400 minutes, and the cost when the talk time exceeds 400 minutes that includes an additional charge per minute over 400.

Here is the piecewise-defined function:

C(t) = { $40, if t ≤ 400 (for talk time up to 400 minutes)
$40 + $0.50(t - 400), if t > 400 (for talk time over 400 minutes) }

In this function, $40 is the fixed cost for the first 400 minutes and $0.50 is the variable cost per additional minute over the 400-minute threshold. The second part of the function calculates the extra fees incurred for the excess minutes used.