Math Example--Exponential Concepts--Graphs of Exponential Functions: Example 1

Topic

Exponential Functions

Description

This example demonstrates the graph of the exponential function y = (0.5)^x. The graph shows a decreasing curve with a y-intercept at ( 0 , 1 ). Students are asked to graph the y-intercept and determine if the function is decreasing or increasing.

Exponential functions are a crucial topic in mathematics, particularly in algebra and calculus. These functions model various real-world phenomena, such as population growth, radioactive decay, and compound interest. By examining multiple examples of exponential function graphs, students can develop a deeper understanding of their behavior and characteristics.

Providing students with multiple worked-out examples is essential for mastering the concept of exponential functions. Each example reinforces key ideas while introducing slight variations, allowing students to recognize patterns and build a comprehensive understanding of how different parameters affect the graph's shape and behavior.

Teacher Script: "Let's look at our first example of an exponential function graph. Notice how the curve starts at ( 0 , 1 ) and decreases as x increases. This is because our base, 0.5, is less than 1. Can you predict what would happen if we used a base greater than 1? In the following examples, we'll explore different bases and how they affect the graph's behavior."

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