# Day 97: The Delight of the Engaged Student!

Two things happened today that makes me so thankful for the students I teach!  During both precalculus block periods, we continued our study of logarithmic and exponential functions including applications and advanced uses of the properties.  The first thing was my students’ tenaciousness toward solving the “HPC 3.3 Hillside Retaining Wall Problem” that I give every year.  Its adapted from a university precalculus problem I found that combines linear, geometric series and logarithms to eventually solve the problem.

I gave approximately 10 minutes of the block time for them to collaborate and discuss what they had done so far.  They we using phrases like: “I really don’t know where to start, but I was thinking…,” “What I did was…,” “Oooh! So its like…,” “So you made x equal to…,” followed by “No, I made it ___ because …,” “That makes sense because…,” “YES! (both hands in the air) I got it!”  Such lively and academic conversations!  So COOL!!  Like McDonalds, I’m lovin’ it.

The second awesome thing was a student was really intrigued with Euler’s equation eπi =-1 and how it could help solve the equation 3=-27.  Below was the final exploration and results.  So COOL! again.