We recently started in on sequences and the book opens the chapter with problems that require students to create a table and come up with a pattern. The first one was about multiplying bunnies. The problem stated that we start off with two bunnies and, each month, each pair of bunnies has two babies. The problem wanted students to figure out how many bunnies there would be at the end of 12 months, as well as to determine the pattern and what family of equations described the growth.
I had one student who fairly quickly completed the problem. One of the extension questions that the textbook suggested was for students to attempt to write an equation that represented the situation. This student, after he graphed the growth, recognized that it wasn’t a linear growth pattern. When asked if the situation could be represented by a straight line, he said no, it was something else. However, when he was set to the task of determining an equation for the situation, he always came up with a linear equation. When I asked him what the graph of his equation would look like, he knew it would be a line. When I showed him the basic exponential equation (y=b^x), he recognized that was the form he needed to use, but even by the end of class all of the equations he was creating were linear equations.
I didn’t expect him to come up with the correct equation, but it was interesting to me that he was constantly writing linear equations. If I had been able to sit with him, he probably could have been guided to finding the correct equation. It just wasn’t possible for me to do that. I know that it is a topic covered later on in the chapter, and in another chapter in the textbook, so I know that he’ll eventually have the opportunity to work with the concept more.