Math Example--Exponential Concepts--Graphs of Exponential Functions: Example 39

Topic

Exponential Functions

Description

This example presents the graph of the exponential function y = 3 * 10^0.5x. The graph displays an increasing curve with a y-intercept at ( 0 , 3 ). Students are asked to graph the y-intercept and determine whether the function is decreasing or increasing.

Exponential functions with base 10 are fundamental in various scientific and engineering applications. By examining this example with both a coefficient multiplying the function and a fractional coefficient 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 coefficients 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-ninth example. We have the base-10 exponential function multiplied by 3, and 0.5x in the exponent. How do these changes affect the graph's behavior compared to our previous examples? Can you explain why the function increases more slowly than y = 3 * 10^x? As we continue exploring more functions with base 10, try to predict how combinations of coefficients outside and fractional coefficients inside the exponential expression will influence the graph's position and rate of increase."

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