Question

The table shows the profit from a school book fair based on the number of books sold.

Books Sold (x) Profit f(x)
100 $50
250 $275
300 $350
350 $425
The rate of change for the function represented by the table is $
per book.

Answer 1

To find the rate of change for the profit based on the number of books sold, we can calculate the profit per book sold between each consecutive pair of points in the table and then find an overall average rate of change.

The formula for rate of change between two points is given by:

\[
\text{Rate of Change} = \frac{\text{Change in Profit}}{\text{Change in Books Sold}} = \frac{f(x_2) - f(x_1)}{x_2 - x_1}
\]

Let's calculate the rate of change for each consecutive pair:

1. Between 100 and 250 books:
- Change in Profit = $275 - $50 = $225
- Change in Books Sold = 250 - 100 = 150
- Rate of Change = \(\frac{225}{150} = 1.5\)

2. Between 250 and 300 books:
- Change in Profit = $350 - $275 = $75
- Change in Books Sold = 300 - 250 = 50
- Rate of Change = \(\frac{75}{50} = 1.5\)

3. Between 300 and 350 books:
- Change in Profit = $425 - $350 = $75
- Change in Books Sold = 350 - 300 = 50
- Rate of Change = \(\frac{75}{50} = 1.5\)

All calculations yield a rate of change of $1.5 per book sold.

Thus, the overall average rate of change, and therefore the rate of change for the function represented by the table, is **$1.50 per book**.