To determine the rate of change for the function represented in the table, we need to calculate the change in profit with respect to the change in the number of books sold. The rate of change for a function can be interpreted as the slope between two points [tex]\((x_1, f(x_1))\)[/tex] and [tex]\((x_2, f(x_2))\)[/tex]. The slope formula is:
[tex]\[
\text{Rate of Change} = \frac{\Delta \text{Profit}}{\Delta \text{Books Sold}} = \frac{f(x_2) - f(x_1)}{x_2 - x_1}
\][/tex]
We will find the rate of change across different intervals:
1. Interval between 100 and 250 books:
[tex]\[
\text{Rate}_{1} = \frac{f(250) - f(100)}{250 - 100} = \frac{275.00 - 50.00}{250 - 100} = \frac{225.00}{150} = 1.5 \, \text{per book}
\][/tex]
2. Interval between 250 and 300 books:
[tex]\[
\text{Rate}_{2} = \frac{f(300) - f(250)}{300 - 250} = \frac{350.00 - 275.00}{300 - 250} = \frac{75.00}{50} = 1.5 \, \text{per book}
\][/tex]
3. Interval between 300 and 350 books:
[tex]\[
\text{Rate}_{3} = \frac{f(350) - f(300)}{350 - 300} = \frac{425.00 - 350.00}{350 - 300} = \frac{75.00}{50} = 1.5 \, \text{per book}
\][/tex]
Since the rate of change is consistent across all intervals, we conclude that the rate of change is [tex]\(\$1.50\)[/tex] per book.
Therefore, the correct rate of change for the function represented in the table is:
[tex]\[\$1.50 \, \text{per book}\][/tex]
So the correct answer is:
[tex]\(\boxed{\$ 1.50 \, \text{per book}}\)[/tex]
