Question

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?
$0.50

$0.67

$1.07

$1.50

Book sold Profit f(x)
(X)
100       ║   $50.00
250      ║      $275.00
300      ║      $350.00
350     ║     $425.00 answer is A-$0.50

Answer 1

Answer: $1.5 per book sold.

Step-by-step explanation:

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

The rate of change for any function $y=f(x)$ is given by :-

$R=\frac{f(x_2)-f(x_1)}{x_2-x_1}\\\\\Rightarrow\ R=\frac{275.00-50.00}{250-100}\\\\\Rightarrow\ R=\frac{225}{150}\\\Rightarrow\ R=1.5$

Hence, the rate of change of the given function is $1.5 per book sold.

Answer 2

You are given a table

$\begin{array}{cc}\text{Number of books sold} & \text{Profit}\\100 & \ 50\\250 & \ 275\\300 & \ 350\\350 & \ 450\end{array}$

The rate of change for the function represented in the table can be calculated using the formula

$\dfrac{y_{i+1}-y_i}{x_{i+1}-x_i},$

where i=1,2,3.

1. When i=1,

$\dfrac{y_2-y_2}{x_2-x_1}=\dfrac{275-50}{250-100}=\dfrac{225}{150}=1.5$

2. When i=2,

$\dfrac{y_3-y_2}{x_3-x_2}=\dfrac{350-275}{300-250}=\dfrac{75}{50}=1.5$

3. When i=3,

$\dfrac{y_4-y_3}{x_4-x_3}=\dfrac{425-350}{350-300}=\dfrac{75}{50}=1.5$

Then the rate of change is $1.5

Answer: correct choice is D.