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

the table shows the profit from a school book fair based on the number of books sold.\nprofit 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.\nprofit 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:

D. $1.50 per book

Explanation:

Step1: Recall rate - of - change formula

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

Step2: Select two points

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

Step3: Calculate $\Delta x$ and $\Delta y$

$\Delta x=x_2 - x_1=250 - 100 = 150$. $\Delta y=f(x_2)-f(x_1)=275 - 50=225$.

Step4: Calculate the rate of change

$m=\frac{\Delta y}{\Delta x}=\frac{225}{150}=1.5$. So the rate of change is $1.50$ per book.