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

the table shows the profit from a school book fair based on the number of books sold. what is the rate of change for the function represented in the table? 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 |\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. what is the rate of change for the function represented in the table? 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 |\n$0.50 per book\n$0.67 per book\n$1.07 per book\n$1.50 per book

Answer

Explanation:

Step1: Recall rate - of - change formula

The rate of change of a function $y = f(x)$ is given by $\frac{\Delta y}{\Delta x}=\frac{f(x_2)-f(x_1)}{x_2 - x_1}$.

Step2: Choose two points

Let's take $(x_1,f(x_1))=(100,50)$ and $(x_2,f(x_2))=(250,275)$.

Step3: Calculate the rate of change

$\frac{f(x_2)-f(x_1)}{x_2 - x_1}=\frac{275 - 50}{250-100}=\frac{225}{150}=1.5$.

Answer:

$1.50$ per book