Math Example--Exponential Concepts--Graphs of Exponential Functions: Example 32

Topic

Exponential Functions

Description

This example illustrates the graph of the exponential function y = 10^2x. The graph shows a rapidly increasing curve with a y-intercept at ( 0 , 1 ). Students are asked to graph the y-intercept and determine if the function is decreasing or increasing.

Exponential functions with base 10 are particularly important in various scientific and engineering applications. By examining this example with a coefficient of 2 in the exponent, students can develop a deeper understanding of how such modifications affect the behavior of base-10 exponential functions.

Providing students with multiple worked-out examples is crucial for mastering the concept of exponential functions. Each example introduces a unique combination of bases and exponents, allowing students to observe how these elements interact to produce different graph characteristics. This approach helps students build intuition and analytical skills necessary for working with exponential functions in diverse contexts.

Teacher Script: "Let's examine our thirty-second example. We have the base-10 exponential function, but now with 2x in the exponent. How does this change the graph's behavior compared to y = 10^x? Can you explain why the function increases more rapidly? As we continue exploring more functions with base 10, try to predict how different coefficients in the exponent will affect the steepness of the curve and compare this to what we observed with base e."

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