Math Example--Exponential Concepts--Exponential Functions in Tabular and Graph Form: Example 32

Topic

Exponential Functions

Description

This math example illustrates the exponential function y = -0.4 * 10^x through both a table of values and a graph. The table presents x-y coordinates for x values from -2 to 2, demonstrating how the function's output changes rapidly as x increases. The accompanying graph provides a visual representation of this exponential growth function, highlighting its distinctive shape and behavior.

Exponential functions are fundamental in mathematics and have numerous real-world applications, such as modeling population growth, compound interest, and radioactive decay. This collection of examples aids in teaching the topic by offering students diverse representations of exponential functions, enabling them to observe how different parameters influence the function's behavior.

The importance of multiple worked-out examples in understanding exponential functions cannot be overstated. Each example in this set showcases a unique form of the exponential function, helping students identify patterns and comprehend how alterations in the base, coefficient, or exponent affect the function's graph and values. This variety of examples strengthens the concept and assists students in developing a more intuitive grasp of exponential behavior.

Teacher Script: "Now, let's look at the function y = -0.4 * 10^x. Notice how the y-values decrease rapidly as x becomes more negative, and increase rapidly as x becomes more positive. This is characteristic of exponential growth, but with a negative coefficient. Compare this graph to the previous example. What similarities and differences do you see? How does the negative coefficient affect the graph's orientation?"

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