Question
How can this function be represented algebraically
Input (boxes) Output (cost)
1 2.25
2 4.50
3 6.75
4 9.00
Input (boxes) Output (cost)
1 2.25
2 4.50
3 6.75
4 9.00
Answers
GPT-4o mini
To find an algebraic representation of the given function, we can analyze the relationship between the input (number of boxes) and the output (cost).
From the data provided:
- For 1 box, the cost is $2.25.
- For 2 boxes, the cost is $4.50.
- For 3 boxes, the cost is $6.75.
- For 4 boxes, the cost is $9.00.
We can observe the following:
- The cost seems to increase linearly as the number of boxes increases.
- To identify the cost per box, we can divide the cost by the number of boxes:
- For 1 box: \( \frac{2.25}{1} = 2.25 \)
- For 2 boxes: \( \frac{4.50}{2} = 2.25 \)
- For 3 boxes: \( \frac{6.75}{3} = 2.25 \)
- For 4 boxes: \( \frac{9.00}{4} = 2.25 \)
The cost per box is $2.25. Therefore, the total cost \( C \) can be represented algebraically as:
\[
C = 2.25n
\]
where \( n \) represents the number of boxes. This function indicates that the total cost is directly proportional to the number of boxes, with a constant of proportionality of $2.25.
From the data provided:
- For 1 box, the cost is $2.25.
- For 2 boxes, the cost is $4.50.
- For 3 boxes, the cost is $6.75.
- For 4 boxes, the cost is $9.00.
We can observe the following:
- The cost seems to increase linearly as the number of boxes increases.
- To identify the cost per box, we can divide the cost by the number of boxes:
- For 1 box: \( \frac{2.25}{1} = 2.25 \)
- For 2 boxes: \( \frac{4.50}{2} = 2.25 \)
- For 3 boxes: \( \frac{6.75}{3} = 2.25 \)
- For 4 boxes: \( \frac{9.00}{4} = 2.25 \)
The cost per box is $2.25. Therefore, the total cost \( C \) can be represented algebraically as:
\[
C = 2.25n
\]
where \( n \) represents the number of boxes. This function indicates that the total cost is directly proportional to the number of boxes, with a constant of proportionality of $2.25.