Average Rate of Change in Exponential Functions

Dr. Nelson's video tutorial explains how to find the average rate of change for exponential functions. It begins with a review of linear functions and their constant rate of change, then contrasts this with the variable rate of change in exponential functions. The video provides step-by-step instructions for calculating the average rate of change over specific intervals and includes a practice problem with a solution to reinforce learning.

What is another term for the rate of change?

• Gradient

• Intercept

• Slope

• Coefficient

What is the significance of the slope in a graph?

• It represents the graph's intercept.

• It indicates the graph's curvature.

• It determines the graph's color.

• It shows the rate at which values increase or decrease.

How does the rate of change in exponential functions differ from linear functions?

• It is constant throughout the graph.

• It decreases over time.

• It is not constant throughout the graph.

• It is always zero.

What formula is used to find the slope or rate of change?

• y2 + y1 / x2 + x1

• y1 - y2 / x1 - x2

• y2 - y1 / x2 - x1

• x2 - x1 / y2 - y1

How do you calculate the average rate of change?

• y1 - y2 / x1 - x2

• x2 - x1 / y2 - y1

• y2 - y1 / x2 - x1

• y2 + y1 / x2 + x1

What was the average rate of change from point C to D?

• 8 to 1

• 28 to 3

• 1 to 8

• 2 to 5

What was the average rate of change from point B to E?

• 4 to 32

• 28 to 3

• 8 to 1

• 2 to 5

What is the first step in finding the average rate of change for an exponential function?

• Drawing the graph

• Filling in the input/output table

• Identifying the interval

• Calculating the slope

What does '2 to the X plus one power' represent in the practice problem?

• The constant rate of change

• The linear function equivalent

• The exponential function to be analyzed

• The slope of the function

What was the average rate of change from point -2 to 2 in the practice problem?

• 8 to 1

• 7.5 to 4

• 1.875 to 1

• 2 to 5