Exponentials and Logarithms

Exponentials

Exponential functions are unique in that they have a variable for their exponent.  The natural exponential function e^x, where e is approximately 2.718, is found in many applications in biology and engineering.

Example: Review of Transformations of Functions Using the Exponential Function

Logarithmic Functions and Their Graphs

Example: Transformations of Exponentials and Logarithms and Their Graphs

Properties of Logarithms

Solving Exponential and Logarithmic Equations 

Graphs of the Basic Exponential and Logistic Functions

Exponential, Base 5

The Natural Exponential Function

Important points on the graph include, (0,1) and (1,e)

The Basic Logistic Function

f(x) = c/(1+ae^(-kx)) 
Important points on the graph include, (0, c/(1+a)) and horizontal asymptotes y = 0 and y = c.