Question
The table shows the profit from a school book fair based on the number of books
sold.
Books Sold (x) - Profit f(x)
10 - $50
25 - $200
30 - $300
35 - $350
The rate of change for the function represented by the table is $_ per book.
NOTE: Type the numerical value into the box to receive credit for this question. DO NOT type the $ into the box, or it will be marked incorrect.
sold.
Books Sold (x) - Profit f(x)
10 - $50
25 - $200
30 - $300
35 - $350
The rate of change for the function represented by the table is $_ per book.
NOTE: Type the numerical value into the box to receive credit for this question. DO NOT type the $ into the box, or it will be marked incorrect.
Answers
GPT-4o mini
To find the rate of change for the function represented by the table, we need to calculate the change in profit divided by the change in the number of books sold.
We can calculate the rate of change between the points given in the table. Let's calculate it between the two points with the most information:
1. From 10 books sold to 35 books sold:
- Profit at 10 books: $50
- Profit at 35 books: $350
- Change in profit: \(350 - 50 = 300\)
- Change in books sold: \(35 - 10 = 25\)
Now, we calculate the rate of change:
\[
\text{Rate of change} = \frac{\text{Change in profit}}{\text{Change in books sold}} = \frac{300}{25} = 12
\]
Thus, the rate of change for the function represented by the table is 12.
We can calculate the rate of change between the points given in the table. Let's calculate it between the two points with the most information:
1. From 10 books sold to 35 books sold:
- Profit at 10 books: $50
- Profit at 35 books: $350
- Change in profit: \(350 - 50 = 300\)
- Change in books sold: \(35 - 10 = 25\)
Now, we calculate the rate of change:
\[
\text{Rate of change} = \frac{\text{Change in profit}}{\text{Change in books sold}} = \frac{300}{25} = 12
\]
Thus, the rate of change for the function represented by the table is 12.