Question

the second movie in the twilight series, new moon, was released in 2009. the chart below shows the box office sales for each of the first four weekends. find the rate of change for each interval. express your answers as decimals rounded to the nearest tenth, if necessary.

weekend	box office sales (in millions)
2	$42.9
3	$15.4
4	$7.9

Explanation:

Step1: Define rate of change formula

The 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, \(x\) is the weekend number and \(y\) is the box office sales (in millions).

Step2: Interval 1 to 2

For weekend 1 (\(x_1 = 1\), \(y_1 = 142.8\)) and weekend 2 (\(x_2 = 2\), \(y_2 = 42.9\)):
\(\frac{42.9 - 142.8}{2 - 1}=\frac{-99.9}{1}=-99.9\)

Step3: Interval 2 to 3

For weekend 2 (\(x_1 = 2\), \(y_1 = 42.9\)) and weekend 3 (\(x_2 = 3\), \(y_2 = 15.4\)):
\(\frac{15.4 - 42.9}{3 - 2}=\frac{-27.5}{1}=-27.5\)

Step4: Interval 3 to 4

For weekend 3 (\(x_1 = 3\), \(y_1 = 15.4\)) and weekend 4 (\(x_2 = 4\), \(y_2 = 7.9\)):
\(\frac{7.9 - 15.4}{4 - 3}=\frac{-7.5}{1}=-7.5\)

Answer:

• Interval 1 - 2: \(-99.9\)
• Interval 2 - 3: \(-27.5\)
• Interval 3 - 4: \(-7.5\)