Question

3. A phone company set the following rate schedule for an m-minute

Answer 1

The obtained answers for the given piecewise function are:

(a) The cost of a call that is under six minutes is 0.70 (m < 6)

(b) The cost of a 14-minute call is 2.62 (m > 6; m is an integer)

(c) The cost of a 9 1/2 minute call is 1.66 (m > 6; m is not an integer)

What is a piecewise function?

A piecewise function is given by different functions at different intervals.

Calculation:

It is given that,

phone company set the following rate schedule for an m-minute call from any of its pay phones.

C(m) = 0. 70 when m ≤ 6

        = 0.70 + 0.24(m - 6) when m > 6 and m is an integer

        = 0.70 + 0.24([m - 6] + 1) when m > 6 and m is not an integer

(a) The cost of a call that is under six minutes:

Since m < 6, the cost is C(m) = 0.76

Thus, the cost of a call that is under six minutes is 0.76

(b) The cost of a 14-minute call:

Since 14 > 6, the cost is C(m) = 0.70 + 0.24(m - 6) when m > 6 and m is an integer.

C(14) = 0.70 + 0.24(14 - 6)

        = 0.70 + 0.24(8)

        = 0.70 + 1.92

        = 2.62

Thus, the cost of a 14-minute call is 2.62.

(c) The cost of a 9 1/2 minute call:

9 1/2 = 19/2 = 9.5

Since 9.5 > 6, the cost is C(m) = 0.70 + 0.24([m - 6] + 1) when m > 6 and m is not an integer.

C(9.5) = 0.70 + 0.24([9.5 - 6] + 1)

          = 0.70 + 0.24([3.5] + 1)

Since we know that if [x] is a function then its domain is R and the range is Z(integer)

So, [3.5] = 3(is an integer)

Then,

C(9.5) = 0.70 + 0.24(3 + 1)

          = 0.70 + 0.96

          = 1.66

Therefore, the cost of a 9 1/2 minute call is 1.66.

Learn more about piecewise function here:

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