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 of the profit based on the number of books sold, we can calculate the change in profit divided by the change in the number of books sold over the intervals provided.

Let's calculate the rate of change between the given data points.

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: \(\frac{75}{50} = 1.5\)

From the calculations above, the rate of change for the function represented by the table is **$1.5 per book**.