Should I be showing formulas like y = a(1+r)^ t when going over exponential and decay functions? It does not seem so because I do not find it in any Geometry book I haver so far. Seems like more of a pre-calc thing. Not that I do not want to enrich them, but there seems to be more than enough material to try to cover anyway.

Check your state standards. My sophs haven't seen exponential functions yet, so it would be too much of a stretch. We teach that in Precalc.

We introduce exponential growth/decay in Algebra I and again in Algebra II. If you're asked to teach it in geometry (which there is a lot of algebra in geometry), I would certainly present the equations behind the graph. On a side note, this is my favorite subject to teach and it is very easy to teach with real world examples such as.... Growth of Savings Account/Retirement Account Interest Decay of Radioactive Materials Decay of Drug Concentrations in the Body Decay of Car Values Growth of the U.S. National Debt Growth of Bacterial Cells etc

y = a(1+r)^ t is actually more related to geometric sequences. But I still don't think I learned these formulas until pre-calc. I don't have much to work with in terms of state standards except for this TechPaths website and whatever objectives are mentioned on the online textbook, EPIC. So, it's very confusing and I have to keep constantly making judgment calls.

y = a(1+r)^ t Technically speaking, that is the compound interest equation. a is the starting amount, r is the interest rate and t is the number of compounding periods. You are quite correct in that this is a judgement call. I wish you well.