Question
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
Answered by
GPT-4o mini
The function \( N(b) \) represents the number of nails Kinsley will have based on the number of boxes \( b \) she purchases. Given that each box contains 150 nails and Kinsley can purchase up to 12 boxes, we can define the domain of \( N(b) \).
1. \( b \) must be a non-negative integer (since Kinsley cannot purchase a negative number of boxes).
2. The maximum number of boxes she can purchase is 12.
Thus, the values \( b \) can take are the integers from 0 to 12, inclusive.
Therefore, the domain of \( N(b) \) is:
\[
\{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12\}
\]
In interval notation, it can also be expressed as:
\[
[0, 12]
\]
This indicates that \( b \) can take any integer value starting from 0 up to 12.
1. \( b \) must be a non-negative integer (since Kinsley cannot purchase a negative number of boxes).
2. The maximum number of boxes she can purchase is 12.
Thus, the values \( b \) can take are the integers from 0 to 12, inclusive.
Therefore, the domain of \( N(b) \) is:
\[
\{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12\}
\]
In interval notation, it can also be expressed as:
\[
[0, 12]
\]
This indicates that \( b \) can take any integer value starting from 0 up to 12.