Math Example--Exponential Concepts--Graphs of Exponential Functions: Example 34

Topic

Exponential Functions

Description

This example showcases the graph of the exponential function y = 10^0.5x. The graph displays an increasing curve with a y-intercept at ( 0 , 1 ). Students are tasked with graphing the y-intercept and determining 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 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 essential for mastering the concept of exponential functions. Each example presents 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 various contexts.

Teacher Script: "Now, let's look at our thirty-fourth example. We have the base-10 exponential function with 0.5x in the exponent. How does this change the graph's behavior compared to y = 10^x? Can you explain why the function increases more slowly? As we continue exploring more functions with base 10, try to predict how fractional coefficients in the exponent will influence the graph's rate of increase 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.