Question
14
15
Kinsley is helping her parents to build a wooden deck behind her home. She is taking a trip to the hardware store to purchase some supplies. The nails she needs come in boxes of 150, and she has enough money to purchase up to 12 boxes. The function N(b) represents the number of nails Kinsley will have if she purchases b boxes.
What is the domain of N(b)?
Answers
GPT-4o mini
The function \( N(b) \) represents the number of nails Kinsley will have if she purchases \( b \) boxes. Given that each box contains 150 nails and Kinsley can purchase up to 12 boxes, we can deduce the domain of \( N(b) \).
The possible values for \( b \) (the number of boxes she can purchase) must:
1. Be a non-negative integer, since she cannot purchase a negative number of boxes.
2. Not exceed the maximum of 12 boxes.
Therefore, the domain of \( N(b) \) can be expressed as:
\[
b \in \{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12\}
\]
In interval notation, this can also be expressed as:
\[
[0, 12]
\]
However, since \( b \) is restricted to whole numbers, it is more accurate to describe the domain as the set of integers from 0 to 12 inclusive.
The possible values for \( b \) (the number of boxes she can purchase) must:
1. Be a non-negative integer, since she cannot purchase a negative number of boxes.
2. Not exceed the maximum of 12 boxes.
Therefore, the domain of \( N(b) \) can be expressed as:
\[
b \in \{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12\}
\]
In interval notation, this can also be expressed as:
\[
[0, 12]
\]
However, since \( b \) is restricted to whole numbers, it is more accurate to describe the domain as the set of integers from 0 to 12 inclusive.