Math Example--Exponential Concepts--Exponential Functions in Tabular and Graph Form: Example 15

Topic

Exponential Functions

Description

This example illustrates the process of creating a table of x-y coordinates and graphing the exponential function y = 1 * 2^0.7x. The image presents both a table of values and a graph plotted on a coordinate plane, with points labeled for x values from -2 to 2. This representation helps students visualize the behavior of an increasing exponential function with a fractional positive exponent.

Exponential functions are a fundamental concept in mathematics, with applications in various fields such as finance, physics, and biology. This collection of examples serves to teach the topic by providing students with diverse representations of exponential functions. By examining different variations of these functions, students can develop a comprehensive understanding of how changes in the equation affect the resulting graph and table of values.

The importance of multiple worked-out examples in mathematics education cannot be overstated. Each example in this series offers a unique perspective on exponential functions, allowing students to recognize patterns and make connections between different representations. This approach helps reinforce key concepts and promotes a deeper understanding of the subject matter, ultimately leading to improved problem-solving skills and mathematical fluency.

Teacher Script: "As we examine this example, pay close attention to how the fractional positive exponent 0.7x affects the graph. Notice how the y values increase as x increases, but at a slower rate than y = 2^x. Can you describe how this graph differs from the ones with whole number exponents? What do you think would happen if we changed the exponent to 0.5x or 0.9x? How would this impact the rate of increase and the overall shape of the curve?"

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