Math Example--Exponential Concepts--Exponential Functions in Tabular and Graph Form: Example 33

Topic

Exponential Functions

Description

This math example showcases the exponential function y = 1 * 10^0.6x through a table of x-y coordinates and a corresponding graph. The table lists values for x ranging from -2 to 2, illustrating how the function's output changes as x increases. The graph provides a visual representation of this exponential growth function, emphasizing its characteristic shape and behavior.

Exponential functions play a crucial role 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.

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.

Teacher Script: "Let's examine the function y = 1 * 10^0.6x. Notice how the y-values increase more rapidly as x becomes positive, and decrease towards zero (but never reaching it) as x becomes negative. This is a hallmark of exponential growth. Compare this graph to the previous examples. How does the coefficient of 1 and the exponent of 0.6x affect the steepness of the curve? Can you predict what would happen if we changed these values?"

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