Question

The function C(d)=8d+2
represents the cost to order a box of donuts d, including the flat rate shipping charge.

a) What is the cost per box of donuts?

b) How much is the flat rate shipping charge?

c) How much will the total cost be to order 3 boxes of donuts?

d) Does finding C(−2)
make sense in the context of this function?

Answer 1

Let's analyze the function \( C(d) = 8d + 2 \).

### a) What is the cost per box of donuts?
The cost per box of donuts is the coefficient of \( d \) in the linear function. Here, it is:
\[
\text{Cost per box} = 8 \text{ dollars}
\]

### b) How much is the flat rate shipping charge?
The flat rate shipping charge is the constant term in the function, which is:
\[
\text{Flat rate shipping charge} = 2 \text{ dollars}
\]

### c) How much will the total cost be to order 3 boxes of donuts?
To find the total cost for 3 boxes, we substitute \( d = 3 \) into the function:
\[
C(3) = 8(3) + 2 = 24 + 2 = 26
\]
So, the total cost to order 3 boxes of donuts is:
\[
\text{Total cost} = 26 \text{ dollars}
\]

### d) Does finding \( C(-2) \) make sense in the context of this function?
The function \( C(d) \) represents the cost of ordering \( d \) boxes of donuts. Since you cannot order a negative number of boxes, finding \( C(-2) \) does not make sense in this context. Thus:
\[
\text{No, finding } C(-2) \text{ does not make sense.}
\]