Math Example--Exponential Concepts--Exponential Functions in Tabular and Graph Form: Example 22
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Algebra >> Exponential and Logarithmic Functions >> Graphs of Exponential and Logarithmic Functions

Math Example--Exponential Concepts--Exponential Functions in Tabular and Graph Form: Example 22

Math Example--Exponential Concepts--Exponential Functions in Tabular and Graph Form: Example 22

Graph and table for y = 3 * 10^(3x)

Topic

Exponential Functions

Description

This math example demonstrates the creation of a table of x-y coordinates and the graphing of the exponential function y = 3 * 103x. The image showcases both a graph and a corresponding table, highlighting the extremely rapid growth of this function. The table includes key points such as (-2, 3 * 10-6), (-1, 0.003), (0, 3), (1, 3000), and (2, 3 * 106), illustrating the dramatic increase in y-values as x increases.

Exponential functions are a fundamental concept in mathematics, with applications in various fields such as finance, physics, and biology. This collection of examples aids in teaching the topic by providing visual and numerical representations of different exponential functions. Students can observe how changes in the base, coefficient, and exponent affect the graph's shape and the rate of growth, developing a more intuitive understanding of these functions.

Presenting multiple worked-out examples is crucial for students to fully comprehend exponential functions. By examining diverse cases, students can identify patterns, compare different functions, and gain a deeper insight into the behavior of exponential relationships. This approach helps reinforce key concepts and enhances students' ability to analyze and interpret exponential functions in various real-world scenarios.

Teacher Script: "Now, let's examine this exponential function, y = 3 * 103x. Can you see how much faster this function grows compared to our previous example? Notice the coefficient 3 and the exponent 3x. How do these affect the graph and the values in our table? Pay attention to how quickly the y-values increase as x changes. This extreme growth is typical of exponential functions with large bases and exponents. How might this function be used to model real-world situations?"

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

Common Core Standards CCSS.MATH.CONTENT.HSF.IF.C.7.E, CCSS.Math.CONTENT.HSF.LE.A.2, CCSS.MATH.CONTENT.HSF.LE.B.5
Grade Range 9 - 12
Curriculum Nodes Algebra
    • Exponential and Logarithmic Functions
        • Graphs of Exponential and Logarithmic Functions
Copyright Year 2015
Keywords function, graphs of exponential functions, exponential function tables