Exponential Functions & Graphs

Hate them or hate them, they're there, aren't they. (What makes an exponential exponential, btw, is that there are x's in the exponents.) I won't try and help you find the joy in these brutes (I've never met a student who didn't think these are hard), but I can tell you with some certainty that you're going to have to learn them because they're covered in the math program of every single school - high school or college - in either Algebra II or Pre-Calc. On the bright side, they're also taught exactly the same at every school, with the same questions, so if you work through all the videos below, you'll be in good shape! (If you're having a rough time figuring out the difference between logs and exponentials, check out the Logarithms chapter, which will focus on how to tell these notorious boogers apart.)

Graphing Exponentials

As with all functions, plugging in points is a great way to graph. Tip: When doing a transformation on an exponential function, do any flips and inversions before vertical and horizontal shifts, and don't forget that exponentials always always always have a horizontal asymptote (logs have vertical).

Compound Interest

Interest as in money, not interest. Compounded monthly. Compounded quarterly. Compounded semi-annually on a quarterly basis daily. The terms get confusing, but I'll get you through A=Pert and A=P(1+e/n)nt and the terminology that goes with it. And hey, you get to use your calculator!

Solving Exponential Equations (by matching bases)

In the logs chapter we'll get into harder problems. This video is about the easier half of exponential equations you'll have to solve: using exponent trickery to manipulate the two sides of the equation to have the same base, thus allowing us to assume the exponents are equal.

Solving Exponential Equations Using Logs

Sometimes you can't match bases to solve exponentials, like in 3x = 5x-7, and you have to take the log of both sides! If you don't know logs yet, you'll need to jump ahead and watch the first few videos on logs in the next chapter before doubling back here.

Word Problems: Exponential Growth & Decay

These problems use logs, so check out the logs chapter first if you're lost on those. The examples I work include exponential growth of a rabbit population, more compound interest, and radioactive decay including working with half-life.

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