Math Example--Exponential Concepts--Exponential Functions in Tabular and Graph Form: Example 27

Topic

Exponential Functions

Description

This math example focuses on creating a table of x-y coordinates and graphing the exponential function y = -0.4 * 10^x. The image displays both a graph and a corresponding table, illustrating the behavior of this negative exponential function with a fractional coefficient. The table includes key points such as (-2, -0.004), (-1, -0.04), (0, -0.4), (1, -4), and (2, -40), demonstrating how the y-values decrease rapidly in the negative direction as x increases.

Exponential functions are a crucial concept in mathematics, with applications in various fields such as physics, economics, and engineering. This collection of examples helps teach the topic by providing visual and numerical representations of different types of exponential functions, including those with negative coefficients and fractional coefficients. Students can observe how these factors affect the graph's shape, the y-intercept, and the function's behavior, developing a more comprehensive understanding of exponential relationships.

Offering multiple worked-out examples is essential for students to fully grasp the concept of exponential functions. By examining diverse cases, students can identify patterns, compare and contrast different functions, and develop a deeper insight into how exponential functions behave in various scenarios. This approach helps reinforce key concepts and improves students' ability to analyze and interpret exponential relationships in different contexts, such as exponential decay processes or financial depreciation models.

Teacher Script: "Let's examine this interesting exponential function, y = -0.4 * 10^x. Notice how it's different from our previous examples. What do you observe about the y-values as x increases? Can you see how the negative coefficient affects the graph? This function demonstrates exponential growth in the negative direction. How might this type of function be used to model real-world situations, such as the accumulation of debt or the spread of negative information?"

For a complete collection of math examples related to Exponential Functions click on this link: Math Examples: Exponential Functions Collection.