Math Example--Exponential Concepts--Exponential Functions in Tabular and Graph Form: Example 31

Topic

Exponential Functions

Description

This math example demonstrates the exponential function y = -1 * 10^-0.7x in both tabular and graphical form. The table provides x-y coordinates for x values ranging from -2 to 2, showing how the function's output changes as x increases. The corresponding graph visually represents this relationship, illustrating the characteristic shape of an exponential decay function.

Exponential functions are crucial in mathematics and real-world applications, as they model scenarios where a quantity grows or decays at a rate proportional to its current value. This collection of examples helps teach this topic by providing students with various representations of exponential functions, allowing them to see how different parameters affect the function's behavior.

Seeing multiple worked-out examples is essential for students to fully grasp the concept of exponential functions. Each example in this collection showcases a different form of the exponential function, 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 develop a more intuitive understanding of exponential behavior.

Teacher Script: "Let's examine this exponential function, y = -1 * 10^-0.7x. Notice how the table shows the y-values getting closer to zero as x increases, but never quite reaching it. This is a key characteristic of exponential decay. Now, look at the graph. Can you see how it reflects the values in the table? This visual representation helps us understand the function's behavior over a wider range of x-values."

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