Question

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

Explanation:

Step1: Recall rate of change formula

The rate of change (slope) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by \(\frac{y_2 - y_1}{x_2 - x_1}\).

Step2: Choose two points from the table

Let's take the first two points: \((x_1, f(x_1))=(100, 50)\) and \((x_2, f(x_2))=(250, 275)\).

Step3: Calculate the rate of change

Substitute into the formula: \(\frac{275 - 50}{250 - 100}=\frac{225}{150} = 1.5\). Let's verify with another pair, say \((250, 275)\) and \((300, 350)\): \(\frac{350 - 275}{300 - 250}=\frac{75}{50}=1.5\). And \((300, 350)\) and \((350, 425)\): \(\frac{425 - 350}{350 - 300}=\frac{75}{50}=1.5\). So the rate of change is consistent.

Answer:

\$1.50 per book