Respuesta :
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.
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