Math Example--Exponential Concepts--Exponential Functions in Tabular and Graph Form: Example 21

Topic

Exponential Functions

Description

This math example focuses on creating a table of x-y coordinates and graphing the exponential function y = 1 * 10^2x. The image displays both a graph and a corresponding table, illustrating the rapid growth of this function. The table includes key points such as (-2, 0.0001), (-1, 0.01), (0, 1), (1, 100), and (2, 10,000), demonstrating how quickly the y-values increase as x increases.

Exponential functions are a crucial topic in mathematics, particularly in algebra and calculus. They model various real-world phenomena, including population growth, compound interest, and radioactive decay. This collection of examples helps teach the topic by providing visual representations of different exponential functions, allowing students to see how changes in the base, coefficient, and exponent affect the graph's shape and the rate of growth or decay.

Multiple worked-out examples are essential for students to fully grasp the concept of exponential functions. By examining various cases, students can identify patterns, compare and contrast different functions, and develop a deeper understanding of how exponential functions behave. This approach helps reinforce key concepts and improves students' ability to analyze and interpret exponential relationships in different contexts.

Teacher Script: "Let's take a look at this exponential function, y = 1 * 10^2x. Notice how quickly the y-values grow as x increases. Can you see the pattern in the table? As we move from left to right, each y-value is 100 times the previous one. This rapid growth is characteristic of exponential functions with bases greater than 1. How do you think the graph would change if we used a different base or added a coefficient?"

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