Logarithms Lesson 5 Episode 5 (Teachers)

Repeating Your Reasoning

Josh and Arobindo write a logarithmic expression that describes that amount of time it takes the mold on the peanut butter sandwich to increase by a factor of 20.

Episode Supports

Students’ Conceptual Challenges

Early in the episode, Josh and Arobindo write the equation log4(4100  × 20) = x [0:42]. While there is nothing mathematically wrong with the equation, it does not accurately model the time for which it takes the mold to increase by a factor of 20. Josh and Arobindo seem to have some difficulty with the logarithmic notation here, though they do correct this equation by reminding themselves what logarithms mean.

Focus Questions

For use in a classroom, pause the video and ask these questions:

1. [Pause the video at 1:21] Why is the equation log4(4100 × 20) = x not quite right for finding the time it takes the mold to increase by a factor of 20? How would you fix the equation to make it useful for finding that time?
2. [Pause the video at 3:41] How does the growth factor needed to go from 1 gram to 20 grams compare to the growth factor needed to go from 100 hours to 100 + x hours?

Supporting Dialogue

At the end of this episode, Arobindo and Josh work with a diagram that shows the span of time from p hours to p + x hours. Ask your students to discuss how this diagram can be used to show why log420 accurately represents the length of time needed for any amount of mold to increase by a factor of 20.