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Sagot :
a) The piecewise function is:
[tex]C(n) = 12 + 1.40n, n \leq 20[/tex]
[tex]C(n) = 15 + 1.1n, n > 20[/tex]
b) Applying the piecewise function, it is found that it will cost $40.
A piecewise function is a function that has different definitions based on the input.
Item a:
- 20 or fewer cups, fixed cost of $12 for shipping plus $1.40 per cup. Thus, the first definition of the function for the cost of n cups is:
[tex]C(n) = 12 + 1.40n, n \leq 20[/tex]
- For more than 20 cups, price of $1.1 per cup plus a shipping and handling fee of $15. Then:
[tex]C(n) = 15 + 1.1n, n > 20[/tex]
Then, the piece-wise function is:
[tex]C(n) = 12 + 1.40n, n \leq 20[/tex]
[tex]C(n) = 15 + 1.1n, n > 20[/tex]
Item b:
- The cost of 20 cups is C(20).
- It is the first definition, which is valid for [tex]n \leq 20[/tex].
Then:
[tex]C(20) = 12 + 1.4(20) = 12 + 28 = 40[/tex]
It will cost $40.
A similar problem is given at https://brainly.com/question/24815096
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