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?

1 answer

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

a. To find the cost per box of donuts, look at the coefficient of \( d \) in the function. The cost per box of donuts is \( 8 \) dollars.

b. The flat rate shipping charge is the constant term in the function, which is \( 2 \) dollars.

c. To find the total cost to order 3 boxes of donuts, 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 \( 26 \) dollars.

d. Finding \( C(-2) \) does not make sense in the context of this function because \( d \) represents the number of boxes of donuts ordered, and it cannot be negative. Therefore, \( C(-2) \) is not a valid inquiry in this context.