Respuesta :
Answer: [tex]C=80n+145[/tex]
Step-by-step explanation:
Given : A company charges $225 for the first 1000 stickers and $80 for each additional 1000 stickers.
i.e. Cost of first 1000 sticker is fixed as $225.
Rate of 1000 stickers after that = $80
Let C be the total cost ( in dollars) of the stickers as a function of the number n (in thousands) of stickers ordered.
Then, Total cost = Fixed cost of first 1000 stickers+ Cost of stickers after that
[tex]\Rightarrow\ C= 225+(80)(n-1) [/tex]
[tex]\Rightarrow\ C= 225+80n-80 [/tex] [distributive property]
[tex]\Rightarrow\ C= 80n+225-80 [/tex] [commutative property]
[tex]\Rightarrow\ C=80n+145 [/tex]
Hence , the equation that represents the total cost C (in dollars) of the stickers as a function of the number n (in thousands) of stickers ordered. would be
[tex]C=80n+145[/tex]
The linear function that models this situation is given by:
[tex]C(n) = 225 + 80(n-1)[/tex]
A linear function for the cost has the following format:
[tex]C(n) = C(0) + an[/tex]
In which:
- C(0) is the fixed cost.
- a is the slope, that is, the cost per item.
In this problem:
- For the first 1000 stickers, cost of $225, thus [tex]C(0) = 225[/tex].
- For each additional 1000, the cost is of $80, thus [tex]a = 80[/tex], and since this starts for [tex]n > 1[/tex], [tex]n \rightarrow n - 1[/tex].
Then, the function is given by:
[tex]C(n) = 225 + 80(n-1)[/tex]
A similar problem is given at https://brainly.com/question/16302622
