Answers

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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