Math Example--Exponential Concepts--Graphs of Exponential Functions: Example 21

Topic

Exponential Functions

Description

This example showcases the graph of the exponential function y = e^x, where e is the mathematical constant approximately equal to 2.71828. The graph displays an 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 with base e, known as natural exponential functions, play a crucial role in various mathematical and scientific applications, including calculus, physics, and engineering. By examining this fundamental example, students can develop a deeper understanding of the behavior of natural exponential functions.

Providing students with this key example is essential for building a comprehensive understanding of exponential functions. The natural exponential function serves as a benchmark for comparing other exponential functions and is particularly important in calculus and differential equations. This example helps students recognize the unique properties of e as a base and its significance in mathematical modeling.

Teacher Script: "Now, let's look at our twenty-first example. This is the natural exponential function, y = e^x. Notice how it passes through the point (0, 1). Can you explain why this function is always increasing? As we explore more functions with base e, try to consider how this fundamental example relates to other exponential functions we've seen and why it's so important in mathematics and science."

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