In this clip the teacher leads a discussion about what makes a situation exponential.
Introduction to Exponential Functions, Clip 3, 10:56
The teacher has chosen to give the students a situation in which bacteria doubles every 10 minutes even though they have not yet been introduced to the formal definition of an exponential function. They have had some experience with doubling time from the pennie on a checkerboard activity and now they must apply it to a new situation.
In order to help the students, the teacher uses a variable to be 10 minute chunks. This allows the students to come up with the formula quickly and then have to think about how to transform it so the input is in minutes. This allows the teacher to relate function composition to exponential functions, thus revisiting a concept they have already encountered.
She then changes the situation so that the bacteria is going up by 60% every ten minuts followed by decreasing 10% every 10 minutes. This forces the students to think about how the formula will change. Approaching exponential functions in this manner can help the students make sense of the parts of the exponential function by seeing how they relate to the numbers from the context.
