Question

The function C (n) = 12n + 5 gives the cost to order a necklace n, including a flat rate shipping charge. (2 points) What does C (3) represent in the context of this scenario? Which of the following inputs does not make sense in the context of this scenario?

Answer 1

In the context of the function \( C(n) = 12n + 5 \), where \( C(n) \) represents the total cost of ordering necklaces and \( n \) represents the number of necklaces ordered, the input \( C(3) \) represents the total cost to order 3 necklaces. Specifically, it calculates the cost of 3 necklaces plus a flat shipping charge of $5.

To evaluate \( C(3) \):

\[
C(3) = 12(3) + 5 = 36 + 5 = 41
\]

Therefore, \( C(3) \) represents a total cost of $41 to order 3 necklaces.

Regarding the inputs that do not make sense in this context, typically, negative numbers (like \( n = -1 \)), fractions, or non-integer values (like \( n = 2.5 \), if only whole necklaces can be ordered) are inputs that wouldn't make sense in this scenario. Only non-negative integers should be valid inputs since you can't order a negative number of necklaces or a non-whole number of necklaces.