Calculus 1, Lecture 3B: Exponential Functions Fundamental Properties (also see the end of Lec 3A)

Start with a visual based on a property from Lecture 3A. Then move on to discussion of more properties of exponential functions. Brief introduction to Mathematica at the end.

(0:00) Visualizing the "addition to multiplication" property of exponential functions.
(3:08) Exponential functions are often written in alternative ways, including using the number e as a base and having a continuous growth rate.
(9:26) Doubling time and half life.
(15:47) Exponential functions are continuous and smooth (differentiable). They have a constant relative rate of change. The domain is the set of all real numbers, and if the initial value is positive, the range is the open interval from 0 to infinity. They are one-to-one. If the codomain is considered to be the set of all positive real numbers, then they are onto. Limiting values.
(26:24) Use Mathematica to solve an exponential function, but the output is not in the most ideal form. I will fix this in Lecture 4A.