Math Example--Exponential Concepts--Graphs of Exponential Functions: Example 12

Topic

Exponential Functions

Description

This example showcases the graph of the exponential function y = 2^3x. The graph displays a rapidly increasing curve with a y-intercept at ( 0 , 1 ). Students are tasked with graphing the y-intercept and determining if the function is decreasing or increasing.

Exponential functions play a crucial role in various mathematical and real-world applications, from compound interest calculations to modeling population growth or decay. By examining diverse examples of exponential function graphs, students can develop a nuanced understanding of how different parameters influence the function's behavior.

Providing multiple worked-out examples is essential for students to fully grasp the concept of exponential functions. Each example presents a unique combination of bases and exponents, 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 various contexts.

Teacher Script: "Now, let's look at our twelfth example. We have the same base as the previous example, but now it's raised to the power of 3x. How does this change the graph's behavior? Can you explain why the curve increases more rapidly than in Example 11? As we continue exploring more examples, try to predict how changes in the exponent will affect the steepness of the curve."

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