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 $275
30 $350
35 $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 with respect to the number of books sold, we can use the formula for the rate of change, which is:

\[
\text{Rate of Change} = \frac{\Delta \text{Profit}}{\Delta \text{Books Sold}}
\]

We can choose any two points to calculate this. Let's use the points (10, $50) and (35, $425):

1. **Calculate the change in profit**:
\[
\Delta \text{Profit} = f(35) - f(10) = 425 - 50 = 375
\]

2. **Calculate the change in the number of books sold**:
\[
\Delta \text{Books Sold} = 35 - 10 = 25
\]

3. **Now calculate the rate of change**:
\[
\text{Rate of Change} = \frac{375}{25} = 15
\]

Thus, the rate of change for the function represented by the table is **$15 per book**.