Math Example--Exponential Concepts--Graphs of Exponential Functions: Example 25

Topic

Exponential Functions

Description

This example presents the graph of the exponential function y = 2 * 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 , 2 ). Students are asked to graph the y-intercept and determine whether the function is decreasing or increasing.

Exponential functions with base e are fundamental in various mathematical and scientific applications. By examining this example with a coefficient multiplying the entire function, 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 crucial for mastering the concept of exponential functions. Each example introduces a unique combination of coefficients and bases, 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 diverse contexts.

Teacher Script: "Let's examine our twenty-fifth example. We have the natural exponential function, but now it's multiplied by 2. How does this change the graph's behavior compared to y = e^x? Can you explain why the y-intercept is now at (0, 2) instead of (0, 1)? As we continue exploring more functions with base e, try to predict how different coefficients multiplying the function will affect the graph's position and shape."

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