ELF - Exponential Growth & Decay Lesson
Exponential Growth & Decay
In Algebra 1, one of the functions studied was the exponential function. Exponential functions can represent growth or decay.
This is the parent exponential function where b is the base and b≠0.
Similar to other functions, transformations can be applied to exponential functions.
The input (or domain) of the exponential function is the variable in the exponent, and the output (or range) is the number obtained after the computations.
The asymptote (or boundary line) has the equation of y = k.
In exponential growth functions when a is greater than 0, the ends of the graph behave like the following: as x goes to the left forever (negative infinity), the y (or f(x)) approaches the asymptote (y = k) from above ; and as x goes to the right forever (positive infinity), the y (or f(x)) goes up forever (to positive infinity). When a is less than 0, the ends of the graph behave like the following: as x goes to the left forever (negative infinity), the y (or f(x)) goes down forever (to negative infinity); and as x goes to the right forever (positive infinity), the y (or f(x)) approaches the asymptote (y = k) from below.
Note that when we are graphing an exponential function "by hand" that it is best to create a table of values, and the easiest numbers to use are (-2, -1, 0, 1, 2). Once we are more familiar with the behavior of exponential growth and decay function graphs, then using 1 and 0 should be sufficient (along with the asymptote) to help draw a "quick graph."
In this lesson, we will explore the graphs and applications of exponential growth functions and exponential decay functions.
Let's start by watching the following video that introduces us to exponential growth functions and exponential decay functions.
Graphing Exponential Growth and Decay Functions
Now that we have a good understanding of what exponential growth functions and exponential decay functions are, let's watch some videos that explore the graphs of exponential growth functions and exponential decay functions, as well as their various characteristics.
It's now time for us to explore and practice working with the graphs of exponential growth and exponential decay functions.
Graphs of Exponential Growth & Decay Presentation and Practice
Applications of Exponential Growth and Decay Functions
We can apply what we have learned from the graphs of exponential growth and decay functions to real-world problems. To introduce us to some of these applications, watch the following videos that explore the applications of exponential growth and decay functions in real-world problems.
IMAGES CREATED BY GAVS