Math Example--Exponential Concepts--Graphs of Exponential Functions: Example 38

Topic

Exponential Functions

Description

This example showcases the graph of the exponential function y = -5 * 10^3x. The graph displays a rapidly decreasing curve with a y-intercept at ( 0 , -5 ). Students are tasked with graphing the y-intercept and determining if the function is decreasing or increasing.

Exponential functions with base 10 play a crucial role in various scientific and engineering applications. By examining this example with a negative coefficient multiplying the function and a positive coefficient in the exponent, students can develop a deeper understanding of how such modifications affect the behavior of base-10 exponential functions.

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 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 thirty-eighth example. We have the base-10 exponential function multiplied by -5, and 3x in the exponent. How do these changes affect the graph's behavior compared to our previous examples? Can you explain why the function decreases so rapidly? As we continue exploring more functions with base 10, try to predict how the combination of a negative coefficient outside the exponential and a positive coefficient inside will influence the graph's steepness and direction."

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