Chapter+08+Notes

In Chapter 8 we will be looking at functions and equations that deal with exponential growth and decay, as well as their inverses.

In section 1 we are introduced to exponential growth and decay models. The format are relatively simple, with the variable being in the exponent.

This lesson begins to compare graphs of different forms that all relate to exponential growth or decay. The translations of these graphs follow the same patterns that were used in previous sections.

Now we are introduced to a new number: e. This is a number like pi and is used greatly in finance.

Now that we are working with the variable in the exponents we will need a way to undo these expressions and equations. To solve this need we have logarithms, more commonly called "logs."

The graphs of logarithmic functions follow the same rules as other graphs for their translations. Also, These graphs are the inverses of exponential functions.

When we work with logarithms we can use certain laws and properties to simplify them. These properties are the Product, the Quotient, and the Power rules.

We can use exponents and logarithms to simplify and solve equations by using these inverse operations.

Since we already know how to solve using exponents and logarithms, we can adapt our methods to use the base e as well. These equations follow the same rules and principles as common logarithms making this a continuation of section 8.5.