Math Example--Exponential Concepts--Exponential Functions in Tabular and Graph Form: Example 39

Topic

Exponential Functions

Description

This math example showcases the exponential function y = 1 * e^3x 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 rapidly as x increases. The graph provides a visual representation of this exponential growth function with a modified exponent, emphasizing its steep growth curve and behavior.

Exponential functions with modified exponents are fundamental in mathematics and have numerous real-world applications, such as modeling rapid population growth, compound interest with frequent compounding, and certain chemical reactions. This collection of examples aids in teaching the topic by offering students diverse representations of exponential functions, enabling them to observe how different parameters, particularly in the exponent, influence the function's behavior and rate of growth.

The importance of multiple worked-out examples in understanding exponential functions with modified exponents 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, especially in cases where the growth or decay rate is accelerated or decelerated by factors in the exponent.

Teacher Script: "Now, let's analyze the function y = 1 * e^3x. Notice how much more rapidly this function grows compared to our previous e^x examples. The factor of 3 in the exponent significantly increases the growth rate. Compare this graph to y = e^x. How does tripling the exponent affect the steepness of the curve? Can you think of any real-world scenarios where we might see such rapid exponential growth?"

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