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

the table shows the profit from a school book fair based on the number of books sold. profit vs. books sold\n|books sold (x)|profit f(x)|\n|----|----|\n|100|$50.00|\n|250|$275.00|\n|300|$350.00|\n|350|$425.00|\nwhat is the rate of change for the function represented in the table?\n$0.50 per book\n$0.67 per book\n$1.07 per book\n$1.50 per book

the table shows the profit from a school book fair based on the number of books sold. profit vs. books sold\n|books sold (x)|profit f(x)|\n|----|----|\n|100|$50.00|\n|250|$275.00|\n|300|$350.00|\n|350|$425.00|\nwhat is the rate of change for the function represented in the table?\n$0.50 per book\n$0.67 per book\n$1.07 per book\n$1.50 per book

Answer

Answer:

$1.50 per book

Explanation:

Step1: Identify two points from the table.

Let $(x_1, f(x_1)) = (100, 50.00)$ and $(x_2, f(x_2)) = (250, 275.00)$.

Step2: Calculate the change in profit ($\Delta f(x)$).

$$ \Delta f(x) = f(x_2) - f(x_1) = $275.00 - $50.00 = $225.00 $$

Step3: Calculate the change in books sold ($\Delta x$).

$$ \Delta x = x_2 - x_1 = 250 - 100 = 150 $$

Step4: Calculate the rate of change (slope).

$$ \text{Rate of Change} = \frac{\Delta f(x)}{\Delta x} = \frac{$225.00}{150} = $1.50 \text{ per book} $$