Question
(4 points)
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?
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?
Answers
GPT-4o mini
To answer the questions based on the function \( C(d) = 8d + 2 \), let's break it down:
### a) What is the cost per box of donuts?
The cost per box of donuts can be found from the coefficient of \( d \) in the function. Here, \( 8d \) means that each box of donuts costs \$8. Therefore, the cost per box of donuts is **$8**.
### b) How much is the flat rate shipping charge?
The flat rate shipping charge can be identified from the constant term in the function. The constant term is \( 2 \). Therefore, the flat rate shipping charge is **$2**.
### c) How much will the total cost be to order 3 boxes of donuts?
To find the total cost to order 3 boxes of donuts, we substitute \( d = 3 \) into the function \( C(d) \):
\[
C(3) = 8(3) + 2 = 24 + 2 = 26
\]
Therefore, the total cost to order 3 boxes of donuts is **$26**.
### d) Does finding \( C(-2) \) make sense in the context of this function?
In this context, \( d \) represents the number of boxes of donuts ordered. Since it doesn't make sense to order a negative number of boxes, finding \( C(-2) \) does not make sense in the context of this function. Thus, the answer is **No, it does not make sense to find \( C(-2) \)**.
### a) What is the cost per box of donuts?
The cost per box of donuts can be found from the coefficient of \( d \) in the function. Here, \( 8d \) means that each box of donuts costs \$8. Therefore, the cost per box of donuts is **$8**.
### b) How much is the flat rate shipping charge?
The flat rate shipping charge can be identified from the constant term in the function. The constant term is \( 2 \). Therefore, the flat rate shipping charge is **$2**.
### c) How much will the total cost be to order 3 boxes of donuts?
To find the total cost to order 3 boxes of donuts, we substitute \( d = 3 \) into the function \( C(d) \):
\[
C(3) = 8(3) + 2 = 24 + 2 = 26
\]
Therefore, the total cost to order 3 boxes of donuts is **$26**.
### d) Does finding \( C(-2) \) make sense in the context of this function?
In this context, \( d \) represents the number of boxes of donuts ordered. Since it doesn't make sense to order a negative number of boxes, finding \( C(-2) \) does not make sense in the context of this function. Thus, the answer is **No, it does not make sense to find \( C(-2) \)**.