Exponential Functions and The Natural Logarithm

Guided Notes for this lecture

In this course we use various types of functions to model different scenarios. In many cases we will use exponential functions to model a function that occurs in nature. While you all have learned about exponential functions in your pre-requisit courses, this is function that students often have trouble remembering the properties of and so we will review the basics.

Now that we have reviewed the structure of exponential functions, let's look at some examples of how we can use exponential functions in some practice problems.

Since the key structural feature of exponential functions is that the variable appears in the power of a the function, we need to ensure we have all the tools we need to solve for that variable if needed. So now we review the natural logarithm which will help us to solve exponential function problems, and also has some important uses in other ways.

Here are some applications and computational examples of the natural logarithm

At the end of this section you should be able to answer the following questions:

1. What is the general form of an exponential function and how do we identify if a function is an exponential function?
2. How can we apply what we learned in the earlier sections to determine when an exponential function is increasing, decreasing, positive, negative, concave up, or concave down?
3. Under what conditions (think domain and range) can we use the natural logarithm?

Check Your Understanding
You should try these problems before reviewing the solutions to fill in while watching the video.