Math Example--Exponential Concepts--Graphs of Exponential Functions: Example 2

Topic

Exponential Functions

Description

This example illustrates the graph of the exponential function y = ( 0.7 )^3x. The graph displays a decreasing curve with a y-intercept at ( 0 , 1 ). Students are tasked with graphing the y-intercept and determining whether the function is decreasing or increasing.

Exponential functions are a fundamental concept in mathematics, with applications in various fields such as physics, biology, and economics. By studying multiple examples of exponential function graphs, students can develop a deeper understanding of how different parameters affect the shape and behavior of these functions.

Presenting students with a variety of worked-out examples is crucial 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 second example, we have a slightly different exponential function. Notice that the base is still less than 1, but now we have a factor of 3 in the exponent. How does this change the graph compared to our first example? Can you explain why the curve decreases more rapidly? As we continue with more examples, try to predict how changes in the base and exponent will affect the graph's appearance."

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