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 2, 3:07
In this clip notice that the teacher does not tell students whether the 21% (the common answer from students) is right or wrong, but rather attempts to have students justify their answer. In order to have a climate where students are always justifying their solutions, it is important for the teacher to support this behavior when it does not happen spontaneously.
She also presents them with counterexamples when explaining why 21% is not correct (if I multiply my whole salary by three...).
One student raised .07 to the 3rd power. In this case she had the student calculate to see that his conjecture was incorrect.
Even with the group that did the problem correctly she required justification. It is important as a teacher to make sure the students are attempting to justify their solutions so the other students can observe their thinking.
