Understanding Average Rate of Change

The video tutorial explains how to find the average rate of change of weekly receipts for a movie from three to nine weeks after its opening. It involves calculating the slope of the secant line between two points: (3, 50.306) and (9, 16.24). The process includes identifying the points, graphically representing the problem, and performing the calculation to find the slope, which is -5.68 million dollars per week. This indicates a decline in receipts over the specified period.

What is the main objective of the problem discussed in the video?

• To compare receipts of different movies

• To determine the highest weekly receipt

• To calculate the average rate of change of weekly receipts

• To find the total receipts of the movie

What mathematical concept is used to find the average rate of change?

• Tangent line

• Secant line

• Integral

• Derivative

Which two points are used to calculate the slope of the secant line?

• (3, 50.306) and (6, 25.153)

• (3, 16.24) and (9, 50.306)

• (3, 50.306) and (9, 16.24)

• (0, 0) and (9, 16.24)

How do you calculate the change in receipts?

• Divide the ninth week's receipts by the third week's receipts

• Multiply the receipts of the third and ninth weeks

• Add the receipts of all weeks

• Subtract the first week's receipts from the ninth week's receipts

What is the change in weeks used in the calculation?

• 12 weeks

• 9 weeks

• 3 weeks

• 6 weeks

What is the calculated average rate of change of the weekly receipts?

• 3.45 million dollars per week

• -3.45 million dollars per week

• 5.68 million dollars per week

• -5.68 million dollars per week

To how many decimal places is the average rate of change rounded?

• Three decimal places

• Four decimal places

• Two decimal places

• One decimal place

What does the negative sign in the average rate of change indicate?

• Receipts are increasing

• Receipts are fluctuating

• Receipts are constant

• Receipts are declining

Over which weeks is the average rate of change calculated?

• Weeks 1 to 3

• Weeks 5 to 10

• Weeks 3 to 9

• Weeks 2 to 8

What is the unit of the average rate of change calculated?

• Thousands of dollars per month

• Millions of dollars per week

• Dollars per day

• Millions of dollars per year