Math Example--Exponential Concepts--Exponential Functions in Tabular and Graph Form: Example 35

Topic

Exponential Functions

Description

This math example illustrates the exponential function y = 0.8 * 10^-x through a table of x-y coordinates and a corresponding graph. The table lists values for x ranging from -2 to 2, showing how the function's output changes as x increases. The graph provides a visual representation of this exponential decay function, emphasizing its characteristic shape and behavior.

Exponential functions are crucial in mathematics and have wide-ranging applications in fields such as finance, physics, and biology. This collection of examples aids in teaching the topic by presenting students with various representations of exponential functions, allowing them to observe how different parameters affect the function's behavior. By examining both tabular and graphical forms, students can develop a deeper understanding of the relationship between input and output values in exponential functions, particularly in cases of exponential decay.

The importance of studying multiple worked-out examples cannot be overstated when learning about exponential functions. Each example in this set highlights a different aspect of exponential functions, helping students recognize patterns and understand how changes in the base, coefficient, or exponent impact the function's graph and values. This variety of examples reinforces the concept and helps students build a more intuitive grasp of exponential behavior, preparing them to tackle more complex problems and real-world applications involving exponential decay.

Teacher Script: "Let's examine the function y = 0.8 * 10^-x. Notice how the y-values decrease rapidly as x increases, approaching but never quite reaching zero. This is a classic example of exponential decay. Compare this graph to our previous growth examples. How does the negative exponent change the shape and behavior of the function? Can you think of any real-world scenarios where this type of decay might occur?"

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