Math Example--Exponential Concepts--Exponential Functions in Tabular and Graph Form: Example 45

Topic

Exponential Functions

Description

This example showcases the exponential function y = -0.5 * e^x through a graph and table of x-y coordinates. The table provides points (-2, -0.068), (-1, -0.184), (0, -0.5), (1, -1.36), and (2, -3.69), which are plotted on the accompanying graph. Students are tasked with creating this table and graph to visualize the function's behavior.

Exponential functions are crucial in modeling growth and decay processes across various fields. This collection of examples highlights key concepts such as base changes, exponents, and their effects on graph and table representations. By exploring these variations, students can better understand how slight alterations in equations significantly impact outputs, reinforcing their grasp of exponential functions.

Presenting multiple worked-out examples is vital for students to fully comprehend mathematical concepts. It allows them to observe patterns, make predictions, and build confidence in interpreting exponential functions. Engaging with diverse problems helps develop a robust, long-lasting understanding of these important mathematical ideas.

Teacher Script: As you examine this graph and table, consider how the negative coefficient and positive exponent influence the shape and direction of the curve. Discuss with your classmates any trends you notice. Before plotting the points, what predictions can you make about the graph's appearance? How does this example confirm or challenge your initial thoughts?

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