Math Example--Exponential Concepts--Graphs of Exponential Functions: Example 15

Topic

Exponential Functions

Description

This example showcases the graph of the exponential function y = 3 * ( 2 )^x. The graph displays an increasing curve with a y-intercept at ( 0 , 3 ). 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 coefficients, 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 fifteenth example. We have a coefficient of 3 and a base of 2. How does this affect the graph's shape compared to our previous examples? Can you explain why the curve increases more rapidly than some of our earlier examples? As we continue exploring more functions, try to predict how different combinations of coefficients and bases 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.