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 $f(x)$
250	$\\$275.00$
300	$\\$350.00$
350	$\\$425.00$

what is the rate of change for the function represented in the table?

• $\\$0.67$ per book
• $\\$1.07$ per book
• $\\$0.50$ per book
• $\\$1.50$ per book

Explanation:

Step1: Recall rate of change formula

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

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: \(\frac{275 - 50}{250 - 100}=\frac{225}{150}=1.5\)? Wait, no, wait, maybe I made a mistake. Wait, let's check another pair. Let's take (250, 275) and (300, 350). Then \(\frac{350 - 275}{300 - 250}=\frac{75}{50}=1.5\)? Wait, no, wait the options have $1.50. Wait, let's check (300, 350) and (350, 425). LXI2. Wait, but let's check the first pair again: (100,50) and (250,275): LXI3. Oh, so the rate of change is $1.50 per book.

Answer:

\$1.50 per book