Math Example--Exponential Concepts--Graphs of Exponential Functions: Example 33

Topic

Exponential Functions

Description

This example presents the graph of the exponential function y = 10^-3x. The graph displays a rapidly decreasing curve with a y-intercept at ( 0 , 1 ). Students are asked to graph the y-intercept and determine whether the function is decreasing or increasing.

Exponential functions with base 10 are crucial in various scientific and engineering applications. By examining this example with a negative coefficient in the exponent, students can develop a deeper understanding of how such modifications affect the behavior of base-10 exponential functions.

Providing students with a variety of worked-out examples is essential for building a comprehensive understanding of exponential functions. Each example highlights different aspects of these functions, allowing students to recognize patterns and make connections between different representations. This approach helps reinforce key concepts and improves students' ability to analyze and interpret exponential functions in various contexts.

Teacher Script: "In this thirty-third example, we have the base-10 exponential function with -3x in the exponent. How does this change the graph's behavior compared to our previous examples? Can you explain why the function is now decreasing instead of increasing? As we continue with more examples, try to predict how the sign and magnitude of the coefficient in the exponent will affect the graph's appearance and behavior for base-10 functions."

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