Math 205 Lecture 4 - The Linear, Exponential, and Logarithmic functions

Welcome to lecture 4 of Math 205 - Elements of Calculus - Summer 2016.

In today's lecture we continue our discussion about linear functions--functions whose graphs are straight lines. (FYI: another form that is common that was not mentioned is the so-called standard form of a line, ax + by = c.) We review two common formulas for a straight line, and go through a word problem that uses as a straight line as a model. We also talk about when a linear function is appropriate to model a certain situation.

We then move on to talk about exponential functions, which I may refer to at times as "exponentials". These are power functions where the base is constant while the power is a variable. We discuss how these functions behave, including graphs, and when they are useful to use as a model to solve a problem. We also review the basic laws of exponents, which are essential here. We don't actually do any modeling here, but we will do modelling with these kinds of functions after we learn some calculus.

Next, we move on to talking about logarithms. Perhaps best thought about, in this context, as the inverse functions of exponentials. We define them, go over some basic properties, and also their graphs.

We stopped before completing our discussion of logarithms to answer some homework questions on setting up functions. We will pick up next class with logarithms and then move on to talk about Calculus (starting with rates and limits). Yay!

[yobrien]

Thank you for these lectures! They are very engaging and informative :)