Exponentials Lesson 4 Episode 6 (Teachers)

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As in other episodes, Josh and Arobindo seem to readily overcome a common conceptual challenge in understanding exponential functions. In this episode, they make sense of an “invisible 1” [0:59]. Attending to the coefficient in these exponential equations is a necessary step in making sense of the equation in its totality, as the coefficient represents the starting value from which the entire function grows (in this case, that function is the height of the beanstalk after some number days).

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

1. [Pause the video at 0:22] Compare the two equations: y = 3^x and y = 2(3^x). What is significant about the coefficient 2 in the second equation? Is there a similar coefficient in the first equation? How does the 2 affect the height of the beanstalk compared to the beanstalk whose height is given by the first equation.
2. [Pause the video at 2:09] Compare the two equations y = 1.7(3^x) and y = 1.7(4^x). Describe how each beanstalk is growing and compare their growth over some period of time.

1. Ask students to reflect on their list of key ideas from the previous episode (see Supporting Dialogue for Lesson 4, Episode 5) and what they have discussed and watched during this episode. Based on these ideas, ask them to predict how they might write an equation to describe the height of any beanstalk if they know how tall it is on Day 0 and its growth rate for one day. Encourage them to share their ideas, first with a partner, and then with the class.
2. Ask students to think about the equations they’ve seen in this, and other videos. For these equations, what values are possible for y? What values are possible for x? Ask them to consider what the equation y = 2(3^0.5) might represent in the context of the growing beanstalk.