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?
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 analyze the function \( C(d) = 8d + 2 \), let's address each part of your question.
a) **What is the cost per box of donuts?**
The cost function is linear, and the coefficient of \( d \) (which is 8) represents the cost per box of donuts.
**Answer: The cost per box of donuts is $8.**
b) **How much is the flat rate shipping charge?**
The constant term in the function (which is 2) represents the flat rate shipping charge.
**Answer: 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 for 3 boxes, we substitute \( d = 3 \) into the function:
\[
C(3) = 8(3) + 2 = 24 + 2 = 26
\]
**Answer: The total cost to order 3 boxes of donuts will be $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 you cannot order a negative number of boxes, finding \( C(-2) \) does not make sense in this situation.
**Answer: No, finding \( C(-2) \) does not make sense in the context of this function.**
a) **What is the cost per box of donuts?**
The cost function is linear, and the coefficient of \( d \) (which is 8) represents the cost per box of donuts.
**Answer: The cost per box of donuts is $8.**
b) **How much is the flat rate shipping charge?**
The constant term in the function (which is 2) represents the flat rate shipping charge.
**Answer: 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 for 3 boxes, we substitute \( d = 3 \) into the function:
\[
C(3) = 8(3) + 2 = 24 + 2 = 26
\]
**Answer: The total cost to order 3 boxes of donuts will be $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 you cannot order a negative number of boxes, finding \( C(-2) \) does not make sense in this situation.
**Answer: No, finding \( C(-2) \) does not make sense in the context of this function.**