Math Example--Exponential Concepts--Graphs of Exponential Functions: Example 23

Topic

Exponential Functions

Description

This example showcases the graph of the exponential function y = e^-3x, where e is the mathematical constant approximately equal to 2.71828. The graph displays a rapidly decreasing 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 with base e play a crucial role in various mathematical and scientific applications, including calculus, physics, and engineering. By examining this example with a negative coefficient in the exponent, students can develop a deeper understanding of how such modifications affect the behavior of natural exponential functions.

Providing students with multiple worked-out examples is essential for mastering the concept of exponential functions. Each example presents a unique combination of coefficients 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 twenty-third example. We have the natural exponential function, but this time with -3x in the exponent. How does this change the graph's behavior compared to our previous examples? Can you explain why the function is now decreasing instead of increasing? As we continue exploring more functions with base e, try to predict how the sign and magnitude of the coefficient in the exponent will affect 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.