Question

0 4800
1 3840
2 3072
3 2458
4 1966
5 1573
find the average rate of change from week 1 to week 4.
-625
625
-709
709

Explanation:

Step1: Recall the formula for average rate of change

The average rate of change between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is given by \( \frac{y_2 - y_1}{x_2 - x_1} \). Here, \( x \) represents the week and \( y \) represents the value. For Week 1 (\( x_1 = 1 \)) and Week 4 (\( x_2 = 4 \)), we find the corresponding \( y \)-values: \( y_1 = 3840 \) (value at Week 1) and \( y_2 = 1966 \) (value at Week 4).

Step2: Substitute the values into the formula

Substitute \( x_1 = 1 \), \( y_1 = 3840 \), \( x_2 = 4 \), and \( y_2 = 1966 \) into the formula:

$$ \frac{y_2 - y_1}{x_2 - x_1} = \frac{1966 - 3840}{4 - 1} $$

Step3: Calculate the numerator and the denominator

First, calculate the numerator: \( 1966 - 3840 = -1874 \)
Then, calculate the denominator: \( 4 - 1 = 3 \)

Step4: Divide the numerator by the denominator

Now, divide \( -1874 \) by \( 3 \): \( \frac{-1874}{3} \approx -625 \) (rounded to the nearest whole number)

Answer:

-625