In this clip the instructor discusses the where the multiplicative factor comes from in an exponential function and how it works as the input is increased by 1 year.
When the group gives their solution to the above problem, the teacher writes their suggestion on the board to create a discussion.
Multiplicative Factor, Clip 1, 5:21
It is important to demonstrate the multiplicative relationship in exponential functions. This will help give students an understanding of how they work and of the meaning of the base in the function.
Notice how the teacher is reinforcing the term factor which is the way students are to talk about the base in the classroom.
She then uses the slide to exhibit the difference between a constant rate of change and the constant percent change.
This leads to a discussion of why the amount of increases are going up and she then tries to encourage the students to discus the rate of change as increasing. When this does not spontaneously happen, she has the look at the graph and then the average rates of change in order for them to see that the rates are increasing. She did not give the students the answer, but rather changed representations until they saw the characteristic she was trying to promote.
