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 books sold (x) profit f(x) 100 $50.00 250 $275.00 300 $350.00 350 $425.00 $0.50 per book $0.67 per book $1.07 per book $1.50 per book
Answer
Answer:
D. $1.50 per book
Explanation:
Step1: Recall rate - of - change formula
The rate of change of a function $y = f(x)$ is $\frac{\Delta y}{\Delta x}=\frac{f(x_2)-f(x_1)}{x_2 - x_1}$.
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
$\frac{\Delta y}{\Delta x}=\frac{225}{150}=1.5$. So the rate of change is $1.50$ per book.