Math Example--Exponential Concepts--Graphs of Exponential Functions: Example 4

Topic

Exponential Functions

Description

This example presents the graph of the exponential function y = ( 0.3 )^0.2x. The graph displays a 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 are a fundamental concept in mathematics, with applications ranging from financial modeling to scientific research. By studying various examples of exponential function graphs, students can develop a deeper understanding of how different parameters affect the function's behavior and shape.

Providing students with multiple worked-out examples is crucial for mastering the concept of exponential functions. Each example introduces a unique combination of base and exponent, allowing students to observe how these elements interact to produce different graph characteristics. This approach helps students build intuition and analytical skills necessary for working with exponential functions in diverse contexts.

Teacher Script: "Let's examine our fourth example. Notice that we have a base less than 1, but the exponent is a fraction. How does this affect the graph's shape compared to our previous examples? Can you explain why the curve decreases more slowly than in some of our earlier examples? As we continue exploring more functions, try to predict how different combinations of bases and exponents will influence the graph's appearance and behavior."

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