Instantaneous Rate of Change in Coffee Stores

The video tutorial explains how to approximate the instantaneous rate of change in the number of coffee stores for a popular US chain at the beginning of 2003. It uses data from 2000 to 2006 and visualizes the data points on a graph. The tutorial demonstrates how to calculate the slopes of secant lines between 2002-2003 and 2003-2004, and then averages these slopes to approximate the instantaneous rate of change. The final approximation is 869 stores per year.

What is the main task described in the introduction regarding the coffee chain's data?

• To calculate the total revenue of the coffee chain.

• To find the total number of stores in 2006.

• To approximate the instantaneous rate of change at the beginning of 2003.

• To determine the average number of stores added each year.

What does the horizontal axis represent in the visualization?

• The number of stores.

• The revenue of the stores.

• The location of the stores.

• The year.

How is the number of stores described in terms of a function?

• As a function of time.

• As a function of popularity.

• As a function of location.

• As a function of revenue.

What does the instantaneous rate of change represent in this context?

• The total number of stores in 2003.

• The slope of the tangent line at a specific point in time.

• The average number of stores added each year.

• The difference in store numbers between 2000 and 2006.

What is the purpose of calculating the secant slopes?

• To calculate the total number of employees.

• To approximate the slope of the tangent line.

• To determine the average revenue per store.

• To find the total number of stores in 2004.

What is the change in the number of stores from 2002 to 2003?

• 1,996 stores

• 967 stores

• 6,177 stores

• 771 stores

What is the change in the number of stores from 2003 to 2004?

• 6,177 stores

• 1,996 stores

• 967 stores

• 771 stores

How is the average of the secant slopes used in this context?

• To calculate the total number of stores in 2006.

• To determine the average revenue per store.

• To approximate the instantaneous rate of change.

• To find the total number of employees.

What is the final approximation for the instantaneous rate of change in 2003?

• 967 stores per year

• 771 stores per year

• 1,996 stores per year

• 869 stores per year

Why is the approximation of the instantaneous rate of change important?

• It determines the total revenue of the chain.

• It helps in predicting future store openings.

• It finds the most popular store location.

• It calculates the number of employees needed.