Exponential Equations
We will look at one particular kind of graph which is used in geology to describe radioactive decay and in biology to explain the growth of a population, among other places. An equation of the form y=a^x is called an exponential equation due to the fact that x is used as an exponent. Notice that a is a constant which is raised to the power of a variable. In the quadratic, cubic, and quartic equations we've seen, we have seen x raised to various powers. In an exponential equation, x ceases to be used as a base for an exponent and becomes the exponent itself. What are the ramifications of this? Let us examine the behavior of such equations.
Activity: The Growth of Facebook
Examine the website below.
[1] "Facebook is like an infectious Disease"
1. Describe what the article is about.
2. What features of an exponential graph are useful for describing an infectious disease or the rise of Facebook?
3. What equation is used as a constant in the equation that describes the rise of Facebook? What would happen if this constant was smaller? Larger? (for example, .5 or 100)
4. What is the difference between the first equation and corresponding graph and the second equation and corresponding graph? What does the second graph have that the first graph does not?
5. Is the second equation an exponential equation? Why or why not?
Activity: Class Discussion
The questions above will be discussed as a class.
Activity: Online Search
Find three examples of applications of exponential graphs and equations and describe why exponential graphs work well for these applications.
Reflection
What have you learned about exponential equations in real world contexts? What is the relation of an exponential equation?